As requested by @simply-sithel some quick pics of the paring tools I use. To be honest, I am playing favourites here. Mostly I use Schärffix and the scalpel, but I do use all of them depending on what needs to be done. I’m not exceptionally good at sharpening my knives and you definitely want a sharp blade for paring leather.
So the big bonus a scalpel and schärffix have is, you can exchange the blades The Schärffix works with razorblades and you can turn them three times to use each edge on both sides (just don’t forget to mark the side you already used so you don’t loose count or, if the tool is used by more than one person, they know too). Leather is dulling the blade really quickly though so I’m exchanging or re-sharpening my blades really often to avoid the leather from stretching too much or ripping apart.
You don’t neccessarily need a paring tool to work leatherbindings though. You can thin out the parts that need thinning with a sanding plate, that works fine too. It’s less tricky (you basically just need to fix it firmly so your leather stays in place while you’re working), but it takes longer. Which is equally a pro and con, a con because, well, it takes longer, and a pro because you can hardly mess it up without doing so for quite some time.
So basically you can start out with nothing but sanding paper and a cutter knife (for the corners).