I have a mouse with an interesting number of buttons. (Elecom EX-G Pro; I recommend it if you have large hands and like thumb trackballs.)

So I ran xev to see what buttons they mapped to, and chose:

"xvkbd -text "\[XF86Copy]"" m:0x0 + b:8 "xvkbd -text "\[XF86Paste]"" m:0x0 + b:9

which my fingers have learned work everywhere except Chrome. Thanks, Google.