I dont believe you can use an integrated shifter with an old seven speed deraileur though.
My 2c worth, I had a similar vintage bike with 7 speed shimano stuff. He had a set of RSX 7 speed STI's fitted, they looked nice & worked a treat. You may still find these around on ebay or something. They looked well made, alloy, felt better made than new 105 stuff (I'm sure this isn't so).