The point of a digital signature is to announce that you made this document, as it exists at the time of writing. Once a change is made it should no longer identify as signed.
Most institutions don’t use this functionality, despite the usefulness of it. At present, I’d recommend using it for publicly distributed files to protect against bad actors publishing a document that pretends to be yours.
As for legally binding, ask a lawyer. Generally, things are legally binding if they’re signed by all parties. The specifics get funky, but a digital signature is a solid step for announcing that you did this thing at this datetime and a judge should recognize that if it comes down to it. Bonus points if all parties attach their digital signatures.
So, you can work around these things but you're going to run into problems if you do:
-If you reset the router, you need to restore the original password else they'll know
-if they notice you using these devices when you wouldn't have access, they'll remove them further from your reach. Possibly permanently.
-If detected, a larger conflict is likely to be escalated. This includes a loss of the benefit of the doubt in the future.
I'd suggest that this is not the battle to fight. They're likely fighting your apparent obsession with tech. Let them have this battle and continue your fun later.
Try the Stormlight Archive, wheel of time, or mistborn books. Maybe the redwall books if you're younger. Fun and focus can still be had without a computer!