Can I make the top with only 2 needles - no cables? If so, how.
You could do the brim/visor section on 2 needles, but where it says: "Join in a round.", you'll have to use either a set of double-pointed needles or a circular needle.
It also says to use round needles and I only have straight. Is that such a big deal?
Yes, in this case. Unless you wanted to take the time to change the pattern to include a seam at the back (or somewhere...) because you'd have to have a seam if you want to work on straight needles. I suppose it's do-able, but... :shrug:
Good Luck, whatever you decide.