If they’re small trees, then a small-ish hand axe, or camp axe would be more than adequate, but you need space to swing it, just like you would a cat.
A saw, as others have suggested, would probably be better, but a small sharp axe might be handy for splitting the cut logs/branches for burning or whatever.
Gransförs Bruks are the usual ones suggested, they’re excellent hand-forged tools, but there are others.
You could even check out boot sales/tool sales, find an old axe head, clean it up and sharpen it, then carve a new haft for it from some of the wood you’ve sawn already.
There’s a lot of satisfaction to be had from doing that; I’ve got two, one I bought an axe head from eBay, and made a new haft for it, the other was a head with a rotten haft I found in the shed, modified it for carving, and bought a nice haft and fitted it. Both are now very sharp tools, and I have the satisfaction of having put both together myself.
Hultafors axes are well priced, they should have something that would suit:
http://www.casstrom.co.uk/Axes/Hultafors-Agdor-Range
