If this is your first track day you aren't going to be getting anywhere near exploring the limit of your tires or your bike. You are gonna be concentrating on getting comfortable and your technique/suspension more than your tires. Trust me, if you go down, it's not gonna be because of your D220's. Also what you could do is buy some tires trackside, sometimes Michelin sells their DOT race tires trackside, they install them right there, normally for free, and are normally decently priced. Check into it, but you will be fine on your tires you have now. Just enjoy the track, and remember a few key things.
1) Don't have a deathgrip on the bike, loosen up, relax, it will help with stability
2) Get comfortable with countersteering, it helps a ton
3) Don't worry so much about getting your knee down, don't TRY to get your knee down, just let it happen.
4) When you are hanging off in a corner, don't support yourself with your arms, use your outside leg, or forearm on the tank. Also when you are transitioning, make it as smooth as possible, don't upset the bike on quick transitions
5) DON'T PANIC! Panic is what causes wrecks, look through the corner, smoothly roll on the throttle.
6) Most of all HAVE FUN! It's addicting
Honestly I could go on for hours about techniques, but just get comfortable first, then worry about getting quicker lap times. If you lowside (or even highside) don't get discouraged, it happens at the track, that's where you want to have your wrecks, because you learn from them.