It may sound counter intuitive, but keep putting yourself in these 'Sweaty' situations.
I say this from the perspective of someone who does also suffer from anxiety. In fact, I had it so bad when I was at Uni that I decided to drop out (Got so far behind on the work, and I didn't see any point in getting into a lifetime of debt for a shitty degree).
I also DJ, so I can totally relate to you with a similar situation. I play on Pirate radio, and at first, I would leave the studio literally dripping with sweat. I kept at it, because I enjoy it, and now I only sweat when I play in clubs

I'm never by myself on radio, and I know that who I am with also has a keen interest in DJing and music too. So I know they will hear all of my mistakes. This lead me to sort of 'over amplify' what I was thinking/feeling at the time leading me to get nervous and then sweat.
Practice makes perfect, so keep sticking at it. Eventually everything will fall into place and you will soon wonder why you made a big deal out of it.
Also, when you start sweating, try and move your thoughts to your breathing instead of thinking about sweating. I've often found that when nervous etc, 10 calm and controlled breaths can do the world of good (This really helped me with the situation I mentioned, and others).
All the best!