Sandbox verification emails

Have a look at the SandboxPostCopy Interface. It should be possible to have Apex run after the Sandbox is created and then modify the specific User records email address fields.

Instead of relying on the email address (which is "munged" during the sandbox copy), you can use your mobile number and self-verify in the sandbox with a text message. To do so, edit your User record in your production org, and put your cell number in the "mobile" field.

Sandboxes created after that point will properly copy your mobile number. When you log into sandboxes for the first time, you will be given the option to self-verify by receiving a text message to your phone number.