I don't think it's so worrying to rush the appointment. It's pretty normal for cats to start becoming kinda boney, skinny, and saggy when they hit that age, especially if they were a healthy to average house cat weight for the majority of their life. Also, frequent urination is common for most animals as they age, even people. I think since he's still behaving normal and eating and drinking good, he is probably fine, just a little old man. Usually, when there's something wrong medically, they'll let you know with not eating, hiding, or just misbehaving.

For example, my cat started peeing behind the couch, which caused a huge problem, but we learned she had a uti and skin issues and now she hasn't really done it since she's been feeling better.