The English king was forbidden to employ foreign mercenaries, period: even more by cultural taboo than by written law. Even oversea -the German units used during the AWI were theoretically 'allied contingents'.
It would be extremely unwise for a restored Jacobite king, of already brittle popularity, to have foreign troops (even more so if 'Guards'). Now, since Antiquity the best sources of mercenaries are mountainous, harsh countries where agriculture can sustain only a limited population. Highlanders had a long-standing tradition as mercenaries -older than the Swiss one: Swiss became sought after mercenaries only after crushing Charles the Bold and ensuring their independence (1477), while e.g. the French Garde Ecossaise (later Compagnie Ecossaise des Gardes du Corps) of 'Quentin Durward' fame was raised in 1422 at the very last -the Cent-Suisses were formed in 1497. Thus a Jacobite king would rather have a Highlander Guard -though he would have better to dress it in 'English' uniforms, if in bonnet, short jacket and belted plaid they would be resented as foreign barbarians / invaders by the English population.
George *as king of Hanover* could employ Swiss troops -though having them barracked in London with Guard status would certainly be somehow vetoed by the Parliament. But another difficulty is that Swiss units were not recruited by individually enlisting volunteers, but were raised as formed bodies under the strict legal framework of long-standing contracts (Capitulations) between rulers and groups of Swiss cantons. Most of these contracts dated from the 16th C. (1505 for the Papal Guard); they could be renewed, 'enlarged' by dynastic inheritance (from the Bourbon of France and Spain to that of Naples, from Louis XVI to his brothers the Counts of Provence and Artois) but I'm not aware of totally new contracts during the 18th C.. Thus, unless king Georges happens to inherit a country already with Swiss in its service...