Conventional wisdom over at fatwallet is that Chase does a hard pull for everything, even credit limit increase requests. I don't know if you could avoid it.

I like the Chase Professional for cash back at 3% for restaurants, office supply and hardware stores, 1% everywhere else. It is my primary card for the 3% catagories and backup for where my Amex Blue is not accepted. A bonus is that it does not report on your personal credit report, and it came with a nice 15 month 0% purchase deal.

I would recommend browsing the Chase website (along with fatwallet and other CC sites), find a card you like, and call the number on your current card and see if they will convert.