I don't have asthma and have no nasal polyps. How likely is it my mild hives are caused by aspirin and is it safe to take? They come out hours after.

Find out. It is quite possible you are allergic since aspirin is well known to cause this type of allergic reaction. You either need to stop using aspirin altogether, or you need to see an allergist to have the appropriate testing to determine if you really are allergic so the issue can be put to rest.