Sophie's Stew
Jubble Bubble
Ice Cream Machine
Hasee Bounce
All of those games go by quickly (for me anyway), have excellent payout, and are played using only the mouse. I also play Attack of the Revenge, Pterattack, and TROTRODS, but I don't know if any of those games fit your requirements.
Also I'd like to second Petpet Cannonball, even though you've already dismissed it. Come on, now.

You don't even have to finish an entire game to get 667 points, which is the bare minimum score needed to get 1000 NP.
It's not Flash, but you can also get an easy easy 600 NP every day (if you finish it in under five minutes, plus an intelligence boost for your active pet if you're really lucky) from the Faerie Crossword, which you can find all the answers to on many Neopets fansites. Seriously, just Google "Faerie Crossword Answers" and take your pick. Or just go to PPT's front page.
If you don't like any of those suggestions, then I'm sorry, but I can't help you. =\