i think, speaking from experience, that if he is very scared, he is better muzzled. We are having the same problem with one of our dogs. he is a big goofy softy and well liked at the vets but he hates it there and gets very difficult. We know and trust our vets and have been going there for years and we know that if he ever did bite a staff member there, he would have to be treated very differently. I did a course of work with him earlier this year when we went to the vet every day and the staff there met him and gave him treats. I worked with him at home and then at the vets having a muzzle on and being given treats then having the muzzle on at the vets and the vet staff giving him treats. It worked to a point and he is now handleable there but he is still muzzled to be examined or treated, then the muzzle comes off and the vet makes a big fuss of him.
It is up to us to protect our dogs from themselves and if that means a muzzle then that is what it means.
I have no experience of the baby oil thing but have had stitches in 5 different dogs now and they have all been removed with no problem or tugging...personally i don't think it would make enough difference and would suggest that either way you keep your dog safe by using the muzzle.