I think you worry too much about things that don't really matter.
If it's stressing you out so much to have a collar, then don't wear it. Wearing a collar is not a requirement, and no one will think you're any less of a furry for not having one, it's just a thing some people do. If you don't want other people knowing you're a furry, that's fine, don't tell them. I don't make a point of letting people know I'm into furries unless I know they won't have a problem with it, otherwise I don't really see a reason to bring it up to people who don't like it / don't know about it / don't care about it. It's not really something to hide, but there are people out there who don't look too fondly on furries, so it's best not to blatantly advertise it. But, anyway, right, the collar. Judging from what I've seen, it kind of seems like you're only wearing a collar because you think it's a thing that furries have to do. If I'm wrong about that, I apologize, but that's just what it seems like. If this is the case then you should know that it's not necessary, lots of furries don't wear one, and I would discourage it if you're not ready for the judgment that'll come from it. There are people out there who will probably pick fun at you for wearing a collar, so if you're not ready to deal with that then I would say it's not worth it. If you really really want to wear one and only want to hide it from your dad and wear it elsewhere then it's not really that hard to hide a collar. I've seen some people hide them in their shoe or attach them to the belt loops on their pants, some even pass them off as bracelets. Then, of course, there's always the pockets. I feel that I should also mention that the furry fandom is just that: a fandom. It's not something that should rule your life or that you should dedicate your being to, it shouldn't even be something to lose sleep over. Some people like to see being a furry as something that's branded in their soul or something that they should change their life for, but to most people it's not really like that; it's just an interest in anthromorphic characters, whether it be in writing, art, roleplay, or whatever. You should only put into it whatever you're comfortable with, nothing more.