New dog with matted hair and can't get groomed

I went to petco to try to get my dog groomed and they wouldn't do it because he was growling at them. He's a poodle mix (probably shih zoo).
We got him recently and he has very matted fur. We cut a little around his eyes so he can see better. He really needs a haircut.
Is it a bad idea to do it ourselves? We don't want to hurt him. He doesn't like strangers and honestly, I don't think we are going to be able to get him to any time soon even with having a trainer.