If you are singing solo and unaccompanied, does it matter if you don't stay in perfect pitch. There may be a few people around who may notice but I bet they are very few. My bug is that I tend to go up a semitone every few verses and no one has ever complained (yet :)). Just look at it as artistic expression.
You know why operatic singers use so much vibrato? My music teacher told me it was 'cos they can't sing in tune.