Actually, by RAW, it seems possible that only a monk's unarmed strike can be made with any body part. The non-monk unarmed strike, listed with the rest of the weapons, lacks the clause that it can be used with any body part; thus, the wording at least leans towards the non-monk US can only be make with normal hands (mainhand, offhand), though it certainly doesn't come out and say it.
EDIT: Basically what it comes down to is, everything relating to Unarmed Strike - a monk's or anyone else's - is subject to some of the muddiest wording of anything WotC published, and your best bet is to ask your DM, because RAW is ambiguous at best and facepalmingly nonsensical at worst.