Kidney Disease and Aspirin

My 14 1/2 yr old cat was recently diagnosed with early Kidney Disease.
In the past, when given his yearly vaccines, he's always been given a
portion (I don't know how much) of an aspirin because he reacts very
badly otherwise - growling, hissing, etc. for 24-48 hours afterward
(this from a normally mellow cat). Once he started getting aspirin at
shot time, everything was fine. Anyway, now it's shot time again and my
vet (a new one, unfortuantely, as I moved) is saying he can't get
the aspirin because of the Kidney Disease. Is this true? Any other
suggestions?

Kathleen