In my opinion, it depends....
Sometimes the live crayfish that one tends to find are not in the best condition and I think there is lots of evidence that points towards stress having an effect on the immune response- so maybe more risky to feed out if they are in bad shape. Often times, one worries most about parasites crossing over to animals that are closely related. In other words might be more risky to feed a live cray to another crustatean than it is to a fish. They could carry other 'problems' besides parasites though. You could quarantine the crayfish before you feed them out- month would be good, but even a week or two would be better than nothing. The really stressed or sick ones would probably die during that time. Crayfish males don't tend to be overly fond of each other though so that might present a challenge if you have limited space.
You could freeze the crayfish first, which will kill a lot of 'bugs', which brings me back to 'it depends'. What's your goal? If you just want to add another food item for variety perhaps you'd be better off buying frozen crayfish in the grocery store. On the other hand, if you want to give your ray the chance to 'hunt' and get some intellectual stimulation (which I think we tend to overlook for the most part but should probably consider more) the benefit of the live food might outweigh the potential risk... Of course, there are other things that you could do to make it more challenging for them to get their food, and perhaps cut down on boredom, but the more 'weapons in your arsenal' the easier it will be if 'enrichment' is your goal.
You could also culture the crayfish yourself if you have the space....
Sorry for the long answer!