I know that the following word pairs exist:
button – unbutton
tie – untie
Can we use an analogous process with the verb "velcro"?
“Velcro” as a verb is already a verbing and a genericization, which, however popular, doesn’t have quite the currency or flexibility of words in use for centuries. As Catija says, “unvelcro” can easily be understood, but it’s more comfortable for me to keep “velcro” as a noun and say things like this:
I undid the velcro on my sneakers before kicking them across the room.
He ripped open the velcro on his wallet and everyone in the library looked at him.