Personally, I wouldn't let them transfer anything, I'd take care of it myself. Depending on your comfort level.
What are you worried about them transferring?
-contacts? if you have set them up in google they'll transfer automagically when you log into the new phone

(if you don't its WORTH the time to transfer them into google)
- apps? Because of going to ICS I personally plan on doing it the "old" fashioned way and making a list and doing a "fresh" install.
- app data? this one can be tricky, I plan on using titanium back-up for any data (like angry birds) but in general I plan on using it a oppertunity to "clean house" a little bit
- phone data? for call history I plan on letting it go bye-bye, for SMS messages I'll probably down load a SMS back-up program from the market
- other stuff photos etc. I'll transfer onto a folder on my computer and decide what I want to "move" to the new phone...