Did 100% of the swords used at culloden by the jacobite side have basket hilts? or did some have hilts of other types?

Pretty difficult to give an empirical answer as we don't have all the swords that were used.

My gut feeling answer is no, as their side consisted of unregulated troops, i.e. not 'uniform' or adhering to any specific patterns, then there would have been a large degree of individuality governed by budget, fashion and necessity.

Certainly -- there would also have been smallswords, sabers, and hangers (yes, some of the hangers and sabers would have been basket-hilted, but certainly not all of them). The Irish Picquets and Royal Ecossois would most likely have been equipped with hangers, and I imagine the Jacobite horse (Fitzjames and Strathallan's horse and Bagot's Hussars) would have been using sabers of some sort. Any broadsword or backsword, however, would most certainly have been basket-hilted.

Do keep in mind, however, that only about 190 broadswords are known to have been recovered by Government forces after the battle. I don't know how many swords of other types were found, however.....

To echo David, swords of all types were used. And, as he stated, very few were recovered on the battlefield, at least to be listed as captured by the government forces. I suspect the redcoats were souvenir hunters, like most GIs and probably took more than a few home to hang on the wall. However, the number of swords surrendered after Culloden was also relatively small so it can be assumed - always a dangerous thing to do - that most of the Jacobite forces did not have them.

The Highland troops who were actually fully-armed, i.e. with sword, dirk, pistols, targe and muskets, were relatively few in the Jacobite army. By the time of "The '45", the sword was truly obsolete as a military weapon for infantry although troops continued to be equipped with hangers for many years afterward. The improvements in firearms, the development of the socket bayonet and changes in tactics pretty much doomed the sword as a primary weapon. Scottish Highlanders were late to come to that point of view and it cost them dearly.