Well since they both in their 70's now, this isnt in the realm of possibility.
HOWEVER
If this fight takes place in 1968, with both men at the peak of their physical powers, then it gets fun.
Prior to Batman, Adam West was,in his spare time, a powerlifter. If you ever see him in any films he did during that time, his arms are friggin huge. power however, doesnt mean skill.
Shatner IS a genuine martial artist, however I dont know what stage he was at in 1968 in his training.
Prediction:
West. Because of the power, nothing else.