I used the Avent bottles, and they make a sippy cup top for them, with a soft spout. My DD converted over with no fuss whatsoever and then we moved into regular sippys (hard spout) when she was a bit older. Check and see if your bottle manufacturer makes something similar, or if you're using Avent you can pick some of them up.
I wouldn't switch over to straw cups though, they are not watertight like the sippy's are (so you'll have splashing everywhere unless you limit cups to the table), and your little one will drink much faster through them (filling up with drink at dinnertime [instead of food] isn't good, and if they drink juice or something with it, they are done chugging it before their brain gets the signal from their bellies that they aren't thirsty anymore.)
If he really won't touch a sippy, then I'd recommend waiting a couple more months. Maybe emphasize how big kids/grownups use a cup and not a bottle over that time - stuff like that still always works on my DD. = )
Good luck!