One likely problem is OAL. If the magazine and bolt are built specifically for these super-short cartridges, then you're in a world of trouble. That's definitely the case for the featherweight and super shadow in WSSM, but not (IIRC) for the coyote--I may be wrong though.
If the rifle has magazine and bolt made for a short (.308-length) cartridge, then no problem--you can rebarrel and rechamber for any of the WSMs or WSSMs or short-action cartridges based on the H&H Mag case (.350 Rem, 6.5 Rem).
Another option is to build a wildcat. Once I burn out the barrel on my .223 WSSM I plan to turn it into a 6.5 WSSM. The case capacity of the WSSM is somewhere between a .308 and a .30-06, so your wildcat horizons are pretty wide open. Going bigger than .30 creates some problems with OAL and case capacity, but .244, .257 (both already represented in factory cartridges), .264, .277, .284, and .308 would all be viable and very good performers.