Off the top of my head, here's some Greek generals who died in battle:

• Kallimachos of Athens, died at Marathon, 490 BC: "The Athenians prevailed, then followed the fleeing Persians and struck them down. When they reached the sea they demanded fire and laid hold of the Persian ships. In this work Kallimachos the polemarch was slain, a brave man, and of the generals Stesilaos son of Thrasylaos died." - Herodotos 6.113-114

• King Leonidas of Sparta, died at Thermopylai, 480 BC: "Leonidas, proving himself extremely valiant, fell in that struggle and with him other famous Spartans, whose names I have learned by inquiry since they were worthy men (...) There was a great struggle between the Persians and Lakedaimonians over Leonidas' body, until the Greeks by their courageous prowess dragged it away and routed their enemies four times." - Herodotos 7.224.1-225.1

• Kallias of Athens, died at Potidaia in 432 BC: "After the battle the Athenians set up a trophy, and gave back their dead to the Potidaians under truce. The Potidaians and their allies had close to three hundred killed; the Athenians a hundred and fifty of their own citizens, and Kallias their general." - Thucydides 1.63.3

• Xenophon son of Euripides of Athens, died at Spartolos in 429 BC: "The Athenians took refuge in Potidaia, and afterwards recovered their dead under truce, and returned to Athens with the remnant of their army; four hundred and thirty men and all the generals having died." - Thucydides 2.79.7

• Epitadas and Hippagretas of Sparta, died on Sphakteria, 425 BC: "a parley was held between Kleon and Demosthenes and Styphon, son of Pharax, the other side; since Epitadas, the first of the previous commanders, had been killed, and Hippagretas, the next in command, left for dead among the slain, though still alive, and thus the command had devolved upon Styphon according to the law, in case of anything happening to his superiors." - Thucydides 4.38.1

• Lamachos of Athens, died at Syracuse, 415 BC: "Lamachos came to their aid from the Athenian left with a few archers and with the Argives, and crossing a ditch, was left alone with a few that had crossed with him, and was killed with five or six of his men." - Thucydides 6.101.6

• Anaxibios of Sparta, died at Abydos, 389 BC: "Then Anaxibios, judging that there was no hope of safety, (...) said to those who were with him: “Gentlemen, it is honourable for me to die here, but do you hurry to safety before coming to close engagement with the enemy.” Thus he spoke, and taking his shield from his shieldbearer, fell fighting on that spot." - Xenophon, Hellenika 4.8.38-39

• King Kleombrotos of Sparta, died at Leuktra, 371 BC: "The fact that Kleombrotos and his men were at first victorious in the battle may be known from this clear indication: they would not have been able to take him up and carry him off still living, had not those who were fighting in front of him been holding the advantage at that time." - Xenophon, Hellenika 6.4.13

• Pelopidas of Thebes, died at the Dog's Heads, 364 BC: "The foremost of the mercenaries, coming to close quarters with Pelopidas, were beaten back by him; some also were smitten and slain; but most of them fought at longer range, thrusting their spears through his armour and covering him with wounds." - Plutarch, Life of Pelopidas 32.6-7

• Epameinondas of Thebes, died at Mantineia, 362 BC: "As for the Lakedaimonians, when they saw that Epameinondas in the fury of battle was pressing forward too eagerly, they charged him in a body. As the missiles flew thick and fast about him, he dodged some, others he fended off, still others he pulled from his body and used to ward off his attackers. But while struggling heroically for the victory, he received a mortal wound in the chest. As the spear broke and the iron point was left in his body, he fell of a sudden, his strength sapped by the wound." - Diodoros of Sicily, Library of History 15.87.1

• King Agis III of Sparta, died like Boromir at Megalopolis, 333 BC: "He had fought gloriously and fell with many frontal wounds. As he was being carried by his soldiers back to Sparta, he found himself surrounded by the enemy. Despairing of his own life, he ordered the rest to make their escape with all speed and to save themselves for the service of their country, but he himself armed and rising to his knees defended himself, killed some of the enemy and was himself slain by a javelin." - Diodoros of Sicily, Library of History 17.63.4

There are plenty more. It was normal Greek practice for generals to fight in the front ranks, inspiring their men by example. This meant that their mortality rate was shockingly high, but it was the only way to keep their usually untrained and poorly disciplined militia troops in the fight.

Edit: I didn't actually answer your question regarding Themistokles. According to Herodotos, he was on a trireme in the midst of the battle of Salamis; we have no reason to doubt this. Throughout the Classical period, naval commanders also led from the front. Admirals like the Spartan Kallikratidas and the Athenian Chabrias died in battle at sea.

It's not entirely certain because the evidence we have is both limited and extremely hard to trust. We do have examples of more active participation from later in the 5th century however. Thucydides described a debate in the Athenian Assembly, in which the rhetorician Cleon was "pointing at Nicias, son of Niceratus, then general, whom he hated, he tauntingly said that it would be easy, if they had men for generals, to sail with a force and take those in the island, and that if he had himself been in command, he would have done it." [Source] Although this doesn't conclusively prove that generals fought with the army, it does show that they led them and the manner of their leadership was a point of interest for the general public. Yet, in a later book, a battle is described between the Athenians (led by Cleon) and the Spartans (led by Brasidas):

"Upon hearing this he [Cleon] went up to look, and having done so, being unwilling to venture upon the decisive step of a battle before his reinforcements came up, and fancying that he would have time to retire, bid the retreat be sounded and sent orders to the men to effect it by moving on the left wing in the direction of Eion, which was indeed the only way practicable. This however not being quick enough for him, he joined the retreat in person and made the right wing wheel round, thus turning its unarmed side to the enemy. It was then that Brasidas, seeing the Athenian force in motion and his opportunity come ... fell upon and routed the centre of the Athenians, panic-stricken by their own disorder and astounded at his audacity. At the same moment Clearidas in execution of his orders issued out from the Thracian gates to support him, and also attacked the enemy. The result was that the Athenians, suddenly and unexpectedly attacked on both sides, fell into confusion; and their left towards Eion, which had already got on some distance, at once broke and fled. Just as it was in full retreat and Brasidas was passing on to attack the right, he received a wound" [Source]

If we trust Thucydides, we know that generals - at the very least, Brasidas - fought in battle to the point that they obtained wounds. Thucydides himself lived through this period so he's relatively trustworthy, although he provides no concrete evidence for his words. What's more interesting is what he says later in the same book: "Cleon, who from the first had no thought of fighting, at once fled and was overtaken and slain by a Myrcinian targeteer." Cleon died in battle. Even if he was retreating, it shows that generals were there and that there was risk to the job. It's also a fact with a lot more backing than Brasidas' wound; all later historians, for example Xenophon, attest to the fact that Cleon died on the job.

Although this evidence is slightly anecdotal, nowhere does Thucydides say anything along the lines of "this was unusual", which is odd as most historians didn't like Cleon and so him doing something unusual would have warranted comment. Instead, it tells us that generals were typically present at their battles.

Annoyingly, this doesn't quite answer your question. I'm not sure about traditions early in the century, the events described above taking place in the Peloponnesian War (4301-404 BC). What's problematic about the Greco-Persian wars is that we don't have quite so much detail from relatively reliable historians such as Thucydides, or many readily available eyewitness accounts. From what I know, we have to rely far too heavily on Herodotus, whose accuracy brought us the story of three hundred men (probable) fighting two and a half million (extremely unlikely) at Thermopylae [source]. His account is untrustworthy and incredibly anecdotal. He does give us some examples of generals in the fray at Salamis, for example Artemisia (allied to Xerxes of Persia) who supposedly attacked Persian ships to avoid capture by Greeks [Source]. It's an extremely unlikely tale, however, which leads no credence Herodotus' account.

TL;DR: We know that generals were present at battles, but not whether they all engaged in the hand-to-hand, especially in Themistocles' case. He was there at Salamis, however, because that's what he gets a lot of credit for.