How can I remove an old admin account after Migration Assistant transfer?

Migration Assistant will set up the new computer the same as the old one, based on what transfer options you have selected. When the transfers are completed, you can log into the new Mac with the new User Account name (for your wife) and password and delete the old transferred user or leave it in place as a second admin account. No problem.

well it's a given that you can't login with your user account and delete it

but what if you were to login with your wifes account or have her login and delete yours, if it's set to quick user switch then you may need to reboot so the quick user shift would not block your account from being deleted?

My advice is to keep both admin accounts. You don't have to use both, but having two admin accounts reduces the pain if the single admin account goes bad. And there is some subtle system significance the admin account that the Mac "thinks" is the first or primary admin account.

I don't want to have two administrators with certain operations asking for my admin password such as installing software.

That won't happen. There are no different operations for different admins; all admins have the same privileges

FYI, when migrating to the new system, if you did not want your admin user account on the new Mac, then you could have unchecked it so it would not transfer at all.

If you want to have your old user account on the new Mac, but not to be an "admin", then just go into the "Users & Groups" System Settings and turn off the setting "Allow this user to administer this computer". You can only modify this setting for your user account while logged into your wife's admin account.