I think that for me, I would rather have the trainer say something, but in a professional manner. I would like them to address it as, you seem to be having a problem I have seen many times before, that even I had when I first started working out, that I didn't know it would be a good idea to [I don't know what-put on extra deodorant before working out, switch deodorants to a stronger one....whatever] so I'm just passing this information along to you.
That way, it would seem more like just part of learning from the trainer, the same as learning how to properly do pushups or whatever. It's part of a trainer's job, I think, to make the workout experience the best and most productive possible for the client, and advice on physical comfort regarding clothing or sweating too much or whatever could be part of that.
I do have to say, though, that I might question the professionalism of a trainer who is "unhappy" with how his clients smell when working out. I would think that bad smells would be an occupational hazard in that profession and that people shouldn't feel inhibited about working out based on how their sweat smells. (Some people might be in more need of a shower than others after a workout, of course, but during the actual workout, it shouldn't matter.)