I will second bigjus' comment (and thank you bigjus - I was starting to think I was alone in calling out games for that control decision). I played the game for the 3 seconds required to confirm that there wasn't an undocumented attack key, and came straight down here to make that comment.
I feel like I should comment anyway, to provide feedback from another perspective (general UX rather than just specifically the laptop limitation):
A mouse isn't just a substitute for a button, it allows an entirely different style of interaction than a keyboard or gamepad. If the additional gameplay mechanics you mention include things that require pointing/dragging/scrollwheel/etc, then obviously the mouse is the way to go. But if no such interactions are involved, the mouse isn't a particularly intuitive "button" because that's not what a mouse is. And if the concern is that the additional mechanics will need more buttons, I'd be even more concerned about using a mouse as just a button, because then you're limited to two or three buttons - but you could do more with both hands on the keyboard. (and if you are planning anything that might use left and right click at the same time, I'll mention that's not even possible on a trackpad, so the controls move from awkward to impossible at that point).
If the game really does need the mouse, then using the mouse button for attack might well make sense, since you really don't want the player to have to keep switching between mouse and keyboard. But without aimed attacks, it's difficult (for me at least) to imagine a 2D platformer game that would actually benefit from using the mouse.