There really is no point in having just chrome on the ssd when having all temp files on the hdd. It'll run like it's on the hdd. But if you want, you can set up a symbolic link of just the appdata folder. The temp/history/etc can take a couple gb but you shouldn't worry about lifetime. Chrome actually compresses it's history after awhile because it archives. It used to take a couple gb but is usually under 1gb now. Temp files expire and get deleted. Modern 120gb ssds are expected to last around 50 years of normal usage as far as the nand cells dying are concerned. You can delete any browser's history/cache/temp without having to get another software. Chrome is especially good at managing its own files.
To set up a symbolic link, open...