I just moved into an older house with lead in the water. However, the
kitchen sink was replaced recently and is uncontaminated. It's got
very nice faucet fittings. I don't want to add a new faucet or
replace a faucet, but every single undersink water filter I can find
on the web comes with an attached (usually shoddy) faucet.

Is it possible to buy an undersink water filter and attach it to the
existing cold water line and existing faucet?