I did a little digging to try and find an answer for you, but I've had only limited success. The short answer is that, for reasons I will explain shortly, I can't find any particular evidence of a situation where a knight would surprise onlookers by indicating just prior to combat that he wanted to joust à la guerre ("as in war," or à l'outrance, something like "to the utmost," i.e. death) as opposed to à plaisance (or à plaisir, "for pleasure").

First I will caveat all this by saying that, of course, the nature of the medieval tournament varied wildly depending on when and where you look. Courtly jousting existed in some form between roughly the 11th and the 16th centuries. Earlier jousting, which split off from the mêlée to form its own complementary discipline of martial competition around the 13th century, was more often injurious or fatal and more often materialistically motivated by the direct allure of the spoils that could be won by defeating your enemy (his horse, sword, armor, etc). Later jousting was much more focused on chivalrous and rectitudinous behavior, exemplifying the circular relationship between fictionalized chivalric romances and the idealistic knights who tried to enact those values in real life. It was also much safer, partly thanks to the innovation of the "tilt," the barrier between the knights that forced them to ride in a straight line and strike their opponent at an angle as opposed to head-on, increasing the likelihood of breaking the lance and decreasing the likelihood of serious injury.

A bit on the distinction between these two types of combat: jousting à la plaisance seems to have taken place pretty much exclusively at tournaments, while jousting à la guerre could take place at a tournament or, more commonly, between two skirmishing armies. There were indeed different types of lances, as well as armor: for à la plaisance, a knight would use a lance that was rebated (blunted) or coronelled (fastened with a three-pronged tip that distributed the force more evenly), the later being an innovation of the later medieval period. For à la guerre, as the name might imply, you basically used the same lance that you used for straight up killin' dudes on the battlefield. By the Renaissance, things had calmed down a bit and even à la guerre had restrictions to make it less fatal/injurious. (In late medieval Germany, the two formalized styles were called, respectively, Rennen and Stechen (or Gestech). Maximilian I was a big fan of highly stylized jousting.)

Now, to your actual question, which is about the challenges: it seems that at a tournament, the challenges took place well beforehand and the terms were made clear to all parties, all the more abundantly so if it was à la guerre. First of all, the noble personage hosting the tournament assembled his own retinue of knights, who were called the Tenans (Middle French for "those who hold," basically); all those other knights who received the challenge/invitation were called the Venans ("those who come")—basically just the Home and Away teams. A Tenan would only challenge a Venan, and vice versa. A somewhat unexpected—and somewhat suspect—source for the precise nature of the challenges is a 1907 issue of the British Pall Mall Magazine, which cites as its sources "the details as given by Olivier de la Marche, Chastelain, and other fifteenth-century chroniclers" (I have not investigated the primary sources here):

When [the visitors] have arrived and settled down in their quarters, they will send escutcheons with their arms on them to be hung with others of the challenger's on a tree or artificial arrangement at the lists. Next the visitors will go and with their lances touch certain shields hanging on the tree, and denoting by various hues and colours the different sorts of combats which are to take place. Note will be taken of what shields are touched, and by whom, in order that the necessary arrangements may be made.

The early 19th-century British historian Charles Mills, a somewhat breathless and Romantic "follower of Edward Gibbon," corroborates this in his History of Chivalry quoting a challenge issued by the knights of Charles V of France in 1389, from Froissart's Chroniques:

For the great desire that we have to come to the knowledge of noble gentlemen, knights, esquires, strangers, as well of the nation of France, as elsewhere of far countries, we shall be at St. Ingelbertes, in the marshes of Calais, the 20th day of the month of May next coming, and there continue thirty days complete, the Fridays only excepted, and to deliver all manner of knights and squires, gentlemen, strangers of any nation, whosoever they be, that will come thither for the breaking of five spears, either sharp or rockets, at their pleasure; and without our lodgings shall be the shields of our arms, both shields of peace and of war, and whosoever will joust, let him come or send the day before, and with a rod touch which shield he pleases. If he touch the shield of war, the next day he shall joust with which of the three he will; and if he touch the shield of peace, he shall have jousts of peace and of war; so that whosoever shall touch any of the shields shall shew their names to such as shall be then limited by us to receive them. [...]

So it seems that at a tournament (at least in 14th- and 15th-century France), there isn't really a proper mechanism for same-day challenges, be they à la guerre or not. Therefore you might say that such an action would be quite... outré.

As for non-tournament challenges, they were a bit less strictly regulated, but still had their distinctive characteristics. Back to Froissart, telling us of an event during a 14th-century English campaign in France:

Present at the skirmish at Toury in Beauce was a squire of Beauce, a nobleman of great eagerness who advanced himself on his own without the involvement of anyone else, who came to the barriers as he fought and cried to the English, "Is there no gentleman among you who would perform some feat of arms for the love of his lady? If there is, then here I am, ready to go forth fully armed and mounted to tilt with the lance three times, to land three blows of the battle axe, and three strokes of the dagger. So let there be someone who can undertake such a feat, and all for his lady. Now let us see amongst you Englishmen if there be any of you in love." This French squire was named Gauvain Michaille and his words and request were circulated among the English. Then an English squire stepped forward, an able companion and excellent jouster called Joachim Cator, who said, "Yes, I will gladly oblige him, so have him come forth from the castle at once." The lord of Fitzwalter, marshal of the host, approached the barriers and said to Sir Guy le Baveux who was there, "Have your squire come out here, for he has found someone who will happily oblige him, and we will assure him his safety in all respects." Gauvain Michaille rejoiced at these words, and armed himself immediately with the help of the lords who equipped him fully, and mounted a fine horse which they gave to him. Then, attended by two others, he came forth from the castle, his varlets carrying three lances, three battle axes and three daggers. I can assure you that the English stared at him as he emerged, greatly outraged by the exploit, for they never thought that a Frenchman would dare to fight man-to-man.

Yeah, whatever, Froissart. In any case, Mills has a few other examples like this in his book, frequently revolving around formalized declarations of defending a lady's honor or proving one's love or somesuch. These mid-campaign jousts were sometimes a way for squires to win fame and glory, sometimes a way of staving off boredom during a long siege, but almost always à la guerre and between knights of opposing armies.

TL;DR In 14th- and 15th-century France, the host of a tournament would set up his knight's shields in an appointed place, where visitors could come and issue challenges by touching the shields with their lances. Tournament joust challenges do not seem to have been issued or altered on the spur of the moment, but rather a day or two beforehand. Depending on the manner/area/color of the lance-touching, this could be an indication of a joust à plaisance or à la guerre. On campaign, challenges (seemingly always à la guerre) were more verbal and direct. Wow, this is long.