Hammer ons and pull offs are not cheating, and in fact they help take the stress off of the picking hand, can help you play faster, and smoother.

But its really all about the sound that you want. First of all, the melodic exercise that you developed for yourself sounds really nice, so congrats on the creative skills. Second, if I were playing something like this I would definitely go ahead and pick everything out, but make sure that you play it slow enough to see if there are any improvements that can be made in your picking.

For instance, economy picking is an excellent way to play things more efficiently - is there room in this exercise for something like that? don't be afraid to use a combination of techniques in order to achieve your goal.

Finally, don't ever give up :)