This change occurs in the seventeenth century, and it's a fairly straightforward one. At the beginning of the century, you've still got the "musket and pike" armies -- but by the end of the century they're essentially gone. This change was typically gradual, and different armies made the change at different times.

A musket with a bayonet serves as an adequately "pike-like" weapon but with a firepower capacity. It also avoids the complexities of maneuvering musketeers and pikemen in complex formations like the tercios, maneuvers which required a great deal of expertise and training. Plug bayonets seem to be used in battle from a little before 1620 and onwards.

Even before the arrival of the bayonet, one can detect "the beginning of the end" for the pike at the battle of Nieuwpoort in 1600, a first reverse for the previously dominant tercios at the hands of Maurice of Nassau's army. The Nassau forces still have pikes, but it's their use of firepower and cavalry that makes this an historically important battle . . . the tercio's reputation is truly sunk at Rocroi, in 1643, after which point the Spanish begin to transition to modern formations too..

By 1700 and the War of the Spanish Succession, the change is nearly complete, though pikes and bladed weapons can still be found occasionally, European infantries have largely settled on firearms and bayonets-- the development of the ring bayonet allowing for the weapon to be fired makes this even more preferred, as do improvements in firearms.

These changes are part of the transformation that Geoffrey Parker termed "The Military Revolution"; the 17th century is your rough time frame, and just when this change was made varied from army to army. Hayes-McCoy describes how it proceeded in the British Army:

Before the Restoration [1660] a force of infantry in the field consisted of half pikemen and half musketeers. Gradually the number of pikemen grew less until at the end of the century there were normally no more than fourteen to each company, or a proportion of one pikeman to six musketeers. The pike was superseded by the bayonet which when fixed to the musket combined in one weapon the functions of pike and firearm. It was introduced into the British army at the beginning of the last quarter of the 17th century and by 1691 its use was widespread.

Oddly, there's a renewed interest in the pike during the French Revolution, but that's more along the lines of a curiosity than a durable military practice.

See:

Hyland, G. J. “THE ARMY MUSEUMS OGILBY TRUST PRIZE ESSAY: The Development of the Bayonet.” Journal of the Society for Army Historical Research, 1961, pp. xxxvi-xl.

Lynn, John A. “French Opinion and the Military Resurrection of the Pike, 1792-1794.” Military Affairs, vol. 41, no. 1, 1977, pp. 1–7.

Hayes-McCoy, G. A. “The Battle of Aughrim 1691.” Journal of the Galway Archaeological and Historical Society, vol. 20, no. 1/2, 1942, pp. 1–30.

Parker, Jeffrey "The Military Revolution", 2nd edition, Cambridge University Press: 1998

I would like to know the approximate frame of time in which a military would no longer issue it's rank-and-file soldiers weapons specifically for hand-to-hand combat, such as pikes and swords.

While the use of swords and pikes (etc.) as the main weapon for infantry instead of a firearm disappeared with the adoption of a the bayonet, swords (and some other-hand-to-hand weapons) continued to be issued as sidearms to soldiers whose main weapon was a firearm. Sometimes, these were dual-purpose, such as artillery swords for which a major function was clearing brush from firing positions. Sometimes, they were primarily intended for hand-to-hand combat. With the adoption of breech-loading cartridge rifles, these swords became less common.

Even then, swords and other-hand-to-hand weapons were still used. For example, in WW1 trench raids, hand-to-hand weapons were sometimes the weapon of choice, partly because they were quieter than firearms. Sometimes trench-built improvised weapons were used, but purpose-designed factory-made weapons were also issued, such as the WW1 Welsh knife:

• https://collections.royalarmouries.org/first-world-war/type/rac-narrative-134.html

Outside Europe, swords were issued and used deliberately into the mid-20th century, in armies where the primary infantry weapons were magazine-fed rifles. In some cases, this was due to a shortage of rifles, but some soldiers carried both rifle and sword:

• https://i.pinimg.com/564x/38/71/1e/38711efdd8215bd19c09701d33bea69d.jpg

• https://static.wixstatic.com/media/065f0f_8a0fbad3408245c2bba0eb17f33ce7bc~mv2.gif

The tactical use was in close fighting, where such weapons could be superior to a bayonet (since they're much lighter than a bayonet+rifle, and thus faster). An additional motivation is that soldiers without a firearm will close with the enemy as quickly as possible, rather than stopping half-way to return fire (for which reason, infantry attacks in WW1 were made on many occasions with unloaded rifles, so that the attacking troops would get into bayonet range as quickly as possible).

Many navies still carried the cutlass as a weapon, officially intended for hand-to-hand combat, well into the 20th century. The British Royal Navy withdrew the cutlass as a combat weapon in 1936 (keeping it as a ceremonial/dress weapon), and the US Navy in 1949.

Thus, "When did firearms become the standard infantry weapon?" and "When did swords intended for use in hand-to-hand combat stop being issued?" have two quite different answers, centuries apart.