I'm guessing your dog is on one of those retractable leads if he's able to grab hedgehog before you can react (forgive me if l'm wrong).
I would personally rather rehome the dog.
Staffies have an incredibly high pain threshold so the prickles won't put him off once he has grabbed one. I'd block access. Taking a muzzle on and off every few minutes will drive you both mad.
I don't think there is such a thing as a hedgehog deterrent per se, so blocking up the access routes is probably the safest thing to do. Bear in mind that hedgehogs can dig, so bury any blocking material. I had a word with the lady who runs my local rescue and she was sympathetic to your dilemma. She has had a fair few hedgehogs brought in over the last few weeks with puncture wounds caused by dogs.Her only request was that if your dog does get hold of a hedgehog, please do your best to catch it, and contact either your local rescue, or the British Hedgehog Preservation Society. It may appear to be uninjured, but the spines can hide the damage and the wounds can become infected. If there is any other information you would like, either ask on here or pm me, and l will do my best to help