Well, normally a ballast requires a lamp of the same rating. So a 175W lamp belongs on a 175W ballast. There are exceptions, like SON-H lamps which retrofit to merc ballasts of different wattages, because they match the current rating of the less efficient, higher rated mercury lamps. Generally I think as long as the current and voltage that the ballast puts out is at or close to the arc tube's specification, it will run fine. You can even under drive or over drive lamps moderately for a short time without an ill effect. I ran an 80w fluorescent merc on a 70W son ballast for a few days with no noticeable effects.
I assume you do know that a 175W hid lamp of any type will be enormously bright as a desk light, though?!!