Zeroshell in a linux distribution designed to run on an x86 architecture processor. Therefore it will not run on a D-Link router. On top of that, I would be willing to bet that Zeroshell would be far too large to fit onto the DIR-635’s memory.
I think you are confusing ZeroShell with projects like DD-WRT and OpenWRT.
You can look at those, but I don’t think they’ll support your router. Not a lot of D-Link routers work with replacement firmware.
However, you can build your own wireless router with ZeroShell.
You could look at a product like IBT’s FWA7304* appliance with a wifi card installed in it and run ZeroShell on that.
Otherwise, you’ll need a compatible consumer router that works with a replacement firmware like DD-WRT, OpenWRT, Tomato, etc. See the compatibility lists on their websites. The Linksys WRT54G series are the primary models for these projects.
*Not an ad, I just happen to have purchased one after looking for compatible HW myself.