There are vegan strops. I don't know how good they are, though. Best to join a shave forum to ask.
Griggs is a vegan and he shaves, but last I talked to him, he was keeping his razor in shape on .1 micron iron oxide on balsa, which makes for a super keen razor. Kremer pigments sells a big bag of it for about 10 bucks plus shipping - enough to last a decade. It makes an edge so keen for me that it shaves off every little bump on my face.
There's tons of options that are almost as good as leather.
If iron oxide is too keen, you could use a balsa strop with chromium oxide powder or paste once a week and palm strop every day between (there are videos of palm stropping on youtube - alex gilmore of thejapanblade.com does it on his videos - I just can't find one. All you do with a *clean and dry* palm is flatten your hand out so that your palm skin is tight and run the razor over it (drawing the edge, of course, leading edge into the palm would cause a problem).