Dear Resplen,
Interesting experience. If my hands started perspiring, I wouldn't do hands on and would move to hands off position for the clients comfort, and also limit the session and not overdo it as sometimes less is more and/or move to another area of the body. I would also keep a towel nearby.
Also what are your feelings towards this person? Are you putting in alot of effort and/or being empathic, sympathetic, or indifferent etc. And did you have this condition prior to being a Reiki practitioner? I believe there are gels available you could apply to your palm beforehand you could get from a doctor such as a dermatologist or a nutritionist and yes it could definately be a detox for you as well.
peace,
Prosperity