Do you own the car, or have it on lease/HP/finance? Sounds like it's leased.
You DO realise you won't be covered by insurance at all if you bin it (unless you take out specific track day cover) and if someone else throws their car into you they won't be covered and the disclaimer you signed on the way in means you won't be able to pursue them to recover the cost of the damage to your car?
Just checking.
If you're still up for it then plates off or tape over them will reduce the chance of the finance provider finding your car being thrashed in a manner for which is outside the terms of your agreement.
Any track day will take a road car, but in your position I'd not choose a cheap one as you're less likely to find yourself swamped by numpties.
