If you are performing sticky end PCR you do not need any restriction enzymes at all.
Design primers for your acceptor plasmid to 'linearize' it at the ATG and add a unique 4 nucleotide on the full length forward and another unique on on the full reverse primer. Design your promoter fragment primers to have compatible overhangs to that of the vector. And to answer your question: you will have very very poor yields if both are not perfectly complementary.
You will need to phosphorylate the full length primers for the promoter because primers are usually not phosphorylated at the 5' end. Do your PCR, anneal and ligation as per normal.
But if I were you I would switch over to Golden Gate cloning, our lab did a year ago and I have not regretted it one moment.
I have added a diagram below. There was one thing which I overlooked in my original answer: You can get a direct repeat of the overhangs when the two longest products of each annealing reaction combine in a blunt end ligation but that should not affect your expression too much. However I still think that sticky end PCR is not the best way out of this. Blunt end ligation, gibson or my favourite: Golden Gate are all much more powerful techniques