I believe that all of us has gone through the same problem when we first became vegan. Let me start answering your question by saying that we are not a religion. We are free to decide what we want to do. Even though I disagree, I have met people that call themselves vegan but eat cheese from time to time. They have the right to eat cheese some of the time but I do not think that they should call themselves vegan. They are vegetarians and not vegans.
If you decide to use the non-vegan items like belts and shoes, that is your choice. If you want to give them away again that is your choice. You can even destroy them but I personally disagree with that decision but it is your choice. I even know new vegans that had a burial for their non-vegan items. I personally believe that is a waste of resources and of animals losing their life for these item. Is that burial non-vegan? No, again that is your choice. So you have to decide for yourself what to do.
My choice is to use the item until they wear out. I have been a vegan for 17 years and I still have a couple of leather belts and maybe a couple of pairs of leather shoes which I do not wear anymore. I will probably donate them in the future. I have already donated most of my non-vegan items.
I purchased a Nissan Leaf electric car a couple of months ago and it has a little leather trim on it and it bothered me. I know that an electric car does so much to help the environment so I gave in on a car with a little leather. Did you know that all new cars use some animal products in their cars? Please do not feel guilty with whatever decision that you make. There is no right or wrong answer so make the decision that you believe that is right for you.