To activate the opener, your remote sends a more-or-less unique code. (There may be 1,000 or 10,000 or a million different security codes.) This avoids having neighbors open each other's garages. Even if you manage to duplicate your opener's code precisely, can you be certain it never changes?
Old fashioned openers have two screws on the outside, for connecting wires. You short circuit these to activate the opener. If you do not find two screws, then I think you can only succeed by opening up the housing, and finding the relay which activates the opener. Connect your wifi in custom fashion to this relay. Even if you do that, expect it to require more work on your part to make it reliable.