Can you say no when it comes down to signing for equipment because you are not comfortable with that responsibility?

You aren't required to sign for something site unseen. I recently did a Change of Command inventory and I assure you I looked at every piece of equipment scattered over 6 different locations (3 hours apart) and verified serial numbers.

You need the opportunity to do that IOT sign for anything. If you're being bullied into doing so, use the open door policy of your next leader in the CoC. Nobody wants a FLIPL!

AR 710-2, table 2-2 clearly states: "Receipt, turn-in, and issue of property - verify physical counts and verify and list serial numbers..." per occurrence before signing documents.

https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/r710_2.pdf

You need to physically see all pieces of equipment you are signing for. If you have not seen it, you cant sign for it.

Not being comfortable with the responsibility is not a valid reason. You can't simply choose not to sign for equipment that you are responsible for. You also can't be automatically given the equipment either. The property must transfer hands, you have no control over that. How it is annotated and accepted is what you have control over. You absolutely should not sign for property you cannot visually inspect and verify, and you can't be forced to either. That's why those change of command inspections take so long to complete. 30 days is more than enough time to account for and sign for all the property in an S3 section. Any shortages should be noted, FLIPLs and statement of charges initiated, etc. But, you have to sign for the property and you have more than enough time to do it within regulatory guidance to prevent yourself from being liable for missing or broken equipment.