Hi, great question! In my opinion, your guitar should be just fine for surf. You'll be able to get the desired trem and quick dive bomb sounds even with the blocked trem. In my experience, having to pull up on the bar to get a distinct vibrato going is pretty rare, and if you had to replicate it, most people listening wouldn't know the difference.

Surf music is so much fun to play! Most of it was recorded with Strats back in the day, so you should be good to go with the guitar you already have!

Happy surfing!

Mike