in the gem environment (desktop and "cleanly" programmed apps), use the following key combos to simulate a mouse:
alt+arrows -> direction
alt+insert -> left click/hold
alt+clr home -> right click/hold
in case you still have some amiga mice, have a look if any of them has a switch. perhaps it's even got a label like "Amiga/Atari" or "AM/AT". but if it doesn't, it's still worth a try to flip any switches you find and try the mouse on the atari. :-)