how to prevent wyverns from interrupting your boss battles

Wyvern's travel through blocks, using AI similar to worms in the game, so this makes things very difficult. However, there are a few inconsistencies with your question, so we'll try and clear things up:

As a note, I'm using this page for reference.

1. Wyverns spawn at different heights depending on world size:

You say you've tried making it lower, but you have to be REALLY high up, even on a small world, to get wyverns to spawn. If your arena extends into the same height as floating islands, you're simply too high up.

2. Wyverns will not spawn when the player is standing inside player-placed walls. While time consuming and resource heavy, if you insist on having your arena that high up, fill the entire thing with walls. Could be as cheap as dirt walls, and while it won't look pretty, it should do the trick. You'll want to light it all up with plenty of torches so you can see where you're going.

3. Gear up better. If you can't handle a 4000hp Wyvern in Hardmode, you may simply be undergeared. They are not difficult enemies, and can be dealt with rather quickly with weapons that do a lot of piercing damage (such as bows and repeaters with Jester or Holy arrows, flails, and the Shotgun with explosive bullets).

Again, your main issue seems to be that your arena is too high up, and is spawning Wyverns. If your arena is at floating island heights, you're going to get Wyvern spawns.