So if I understand correctly the insert pattern part of your 'key' is stuck in the head of your wheel bolt?
I think they can get that out with a punch and hammer, the head of the locking nut should protect your wheel as it protrudes enough to get a removal tool onto it which will shag that bolt.
They can then remove the bolt and the other 3 on the other wheels & replace them & provide you with the correct locking key for the replacements.
The mech probably air wrenched it up & didn't even notice the key had broken & left part of itself on the bolt.
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