appliedpsych

PSA: As acceptances start to roll in, this is just a friendly reminder to everyone from someone with lots of contract experience, NEVER ACCEPT A POSITION UNTIL YOU HAVE YOUR FUNDING PACKAGE IN WRITING (unless, of course, you are not expecting funding). Even if it is your top choice and you've been dying to go for the last 20 years... I cannot stress enough; get that s**t in writing.  

@KittyCat_PhD, going forward, you will benefit from establishing boundaries early on. You will need to develop tactics that allow you to walk the delicate balance between what you're being asked to do and what you think is the right thing to do.
IRT your current situation, I recommend that you ask yourself "what's at stake?" On the one hand, your advisor wants you to do something that saves (someone) money and (maybe) advances his personal agenda of tweaking his nose at authority from time to time. On the other hand, you are concerned about managing your risk--what happens if you get found out. Potential diagnostic questions include, how would you feel about his request if there were no risk of the ruse being discovered? (Do you not want to do it because you might get caught, or do you not want to do it because it's wrong or do you not want to do it because there's an expanding pattern of rule bending and you want to get off that train?)  Depending on how you answer the question you could put a dollar amount on the price of compromising. 
"Nothing to worry about." You're being too uptight. To me, those are warning flags that this guy doesn't really give a fuck about you. At all. YMMV.

If I was in that situation I'd take the free registration, introduce myself confidently as a postdoc and then feign TOTAL IGNORANCE if called out. "Oh, my boss Prof X handled my registration."  (Honestly, given how cheap most academics are they'll probably be impressed with your ability to get something for free)
If it only costs $20 to register as a non-student or something like that then just tell your PI you'll pay for the registration yourself. If it costs something like $200 and the PI would otherwise be paying for your registration...then either swallow the lie or don't go.