Hi Freq question.

A high frequency attachment for a stick welder gets you a basic DC TIG unit, but still gets you no dynamic amperage control with a foot pedal or gas control.
It will work, but in a limited capacity. I TIG welded off of a couple of car batteries once just to prove a point. You are far better off buying a used small transformer TIG unit such as a Miller Econotig, Syncrowave 180, Syncrowave 200, or Lincoln Squarewave 175, Precisiontig 185, or one of several older inverter based TIG units from Thermal Arc, ESAB, Miller or Lincoln.
An actual TIG machine is far easier to use and easier to configure for TIG welding.
BTW you can build a foot pedal for about $30. You can adapt sewing machine foot pedals, or even guitar foot pedals.

Put in my vote for the Syncrowave 250, a wonderful (if large and heavy) machine. As for foot pedals, the cost related to the fact that they are built like tanks so they survive being kicked around in an industrial environment.