There were some Clans with members on both sides. There were also many individuals who chose to follow HRH Charles Stuart although their Clan did not. Also, every Clan had soldiers with different surnames (i.e. the Camerons would have had MacMillans, MacMartins etc. the MacDonalds (or MacDonnells) of Keppoch had Stewarts and even Campbells as adherents). The Chief of the MacIntosh Clan was an officer in the electors army, while his wife brought out the Clan for the Prince.
The book "Culloden" by John Prebble will give you a good insight into the Rising of 1745, and its tragic end at Culloden.
If you ever get the chance to go there, there is an excellent interpretive centre at the Culloden battlefield, near Inverness. It is a very moving place.
As to your question - I know there were some MacLeods in the Prince's army
" The Camerons, Stewarts of Appin and the Athollmen made up the right flank's first line. The men of Atholl were positioned on the far right "with their flank resting on the dry-stone wall of the Culwhinia enclosure." Between them and the Stewarts was Lochiel's regiment. A reported 700 men, mainly from Lochaber, were there in Lochiel's formation, mostly consisting of Camerons but also known to include a few men from at least the following clans and septs: Fraser, Grants, MacDonald, MacDougall, MacHoule, MacKenzie, MacLachlan, MacLeod, MacMartin, MacMillan, MacNeill, MacOllonie, MacPhee and even a few men from Clan Campbell. Nevertheless, this was a Clan Cameron regiment, accompanied by their septs and various tenants from Lochiel's estate."
from:
http://www.clan-cameron.org/battles/1746_b.html
But I don't know how many were there, or if there were MacAskills. If I remember correctly, the Clan MacLeod did not come out in force for the Prince, but some of the smaller branches did.
MacAskill, I believe, is a sept of the MacLeods of Lewis.
You can also check out "The Muster Roll of Prince Charles Edward Stuart" - although the actual muster roll is far from complete - it will give you a good idea of what Clans were represented.
It is a fascinating story, I'm sure you'll enjoy learning about it.
Slainte,
John