- Wait for fork to occur.
- Get your wallet key.
- Send all your LTC to a brand new wallet with a brand new address.
- Use your old wallet key with their software and the LCC coins will be there.

There are several posts already that outline this in much greater detail. I'd suggest you find and read them.

But yes, they "could" access your old address if they're scammers and their software sends them your info and/or does some other nefarious stuff. That's why you move stuff to a brand new wallet and address before using their software to get access to the LCC.