A "cobbler" is a person who mends shoes. It's kind of an old-fashioned saying, but still used and understood in both British and American English. Otherwise I suppose you could just say "shoe repairman".
The name given to someone who repairs shoes is a Cobbler, although cobbler are generally shoemakers by trade as well as fixing shoes.
cobbler
The person who repairs your car is called a mechanic.machinate
A person who repairs pipes would be a plumber. I have never heard of any person who specifically repairs tape.
a tinker
A plumber.
cobblerA cobbler is someone who repairs shoes.
tattii maker
Shoe repair man A cobbler.
We call him Plumber.
A Monumental Mason
A glazier.