The "s" is indeed unlikely as a Gaelic plural - can't think of an example offhand."seinn" (pronounced "shine"), to play, has forms ending in m, alright, as JTT says - though I'm not familiar with "seanma". "seinm" I know - usually as the what's-it-called verbal noun "playing" or in present participle "ag seinm" meaning, again, playing.

"musician" is uaully translated as "ceoltoir" (sp.?) from "ceol" meaning music. There is also a noun "seinnadoir" (again, spelling uncertain till I check) meaning player.

I'll check older forms when I find my dictionary!

Regards