It may be possible to avoid being fingerprinted. However, the prosecutor may very well want you to be "booked" as a condition of a plea to a petty theft, as booking allows the prior misdemeanor to be used in the future to make a subsequent petty theft a potential felony. You mentioned the dollar amount was under $50.00, and that may very well work to your benefit. There is a Penal Code section, 490.1, that allows petty thefts under $50.00 to be treated as infractions. You may also look into some form diversion, in order to earn a dismissal. It appears that you have concerns about being fingerprinted. I highly recommend that you discuss that in confidence with a qualified criminal defense attorney. You should also be aware that a petty theft conviction can carry some nasty baggage with it, such as: not being able to be bonded; possible licensing issues, etc.
Best of luck.
Unless you're ordered by the judge at some point, you do NOT have to voluntarily go and be fingerprinted. Often, the police will release you on a citation and send you a notice (or tell you at the time of your citation) to appear and be booked and printed. That guarantees that this case will be linked to you on background fingerprint checks, so unless it is court ordered, you may want to NOT do it until you discuss this with your attorney.
If it's a term of a plea deal, then you'll have to do it, but for such a low dollar amount and given the changes in the laws of petty theft with a prior, I'd be surprised if your attorney couldn't work out a favorable disposition and avoid printing.
But... get a lawyer. This is NOT a do it yourself project.