Well, here's the deal. 7mm needles are closer to 10 1/2 or size 11 needles. size 7 needles are 4.5mm so those 7mm are going to be pretty darn big.
size 1 are going to be WAY too small.
3 straight needles won't work because they just don't. they have the knobs on the back and you need to be able to put stitches on one side and take them off the other.
what you CAN do is make a hat flat and then seam up the back. you can try searching KPC
for hats knit on straight needles or try usingthis
pattern without the logo.
hope that helps!