Hybrid crossfire is using the integrated GPU found in some chipsets to work along side a graphics card to improve the performance, it only works with older lower performance cards and isnt supported with the new generation since IGPs are so weak they wouldnt make a difference.
Crossfire is using two graphics cards together to get better performance.
There are lots, there are several P55 boards, and H55/H57 boards, and X58 boards that meet that requirement, most of the reasonably priced AMD boards that sport crossfire come with an IGP like the 890GX board or the 880G boards, the IGP can be nice to have as a back up so im unsure why you want one without it, but there are lots of options available.
AMD unfortunately has not kept up with updating their IGPs (which is strange as they own ATI, which is now AMD...)
The current 4250/4290 date all the way back to the 2400HD chipset, which was mid/low end part even in its day a few years back. It was part of the first DX10 line of cards for ATI.
I would have though they would have included the newer 5450 as an IGP (which is not totally new either as its based of the 4350 in itself is based of the 4550), which would at least allow you to hybrid x-fire with another 5450.
As it stands you are limited t using a 4350 at best with the current IGP, which will still net you sub par performance.
As someone has mentioned the IGP is only good for as a back up, reset the CMOS, plus your monitor into the motherboard, and you got a singla in case your dedicated card fails, otherwise, leave it off.