It depends what operation they have had.
A vasectomy is commonly carried out on healthy men who decide they don't want any (more) children. In this case the link between the vas deferens and the testes is removed, so no sperm get into the ejaculate. There will still be the same amount of ejaculate as before and this can carry any disease which is spread by bodily fluid. (EG hepatitis, HIV.)
If the client has had their prostate removed (i.e. due to prostate cancer) then they will most probably no longer ejaculate. In this case the risk is smaller, but skin-based diseases can still be passed on, for example herpes and HPV (genital warts.)