As far as compression, you can usually tell by how the saw pulls when starting it. Make sure you have a gauge with a schrader valve right at the tip of the spark plug adapter or you will get a low reading every time. I've seen a 20psi drop with the wrong type of gauge to be pretty common. With a larger displacement cylinder like in a car, there is enough volume that any gauge will work. Not so on small engines.
As far as the BB kits go, I wouldn't touch one for free. I am a Stihl dealer and I have looked at several of the BB kits, in hopes of finding lower cost parts for doing repairs. I would rather throw a saw in the trash, that put a BB kit on it. The cylinder to piston fit is poor, the cylinder wall finish is poor, the ring quality is poor, the piston pins aren't a tapered design and are heavy, and the wrist pin clips have been know to fail and take out the whole upper end.
If you do find that you have low compression, you can get the standard 460 cylinder to fit with modification. I've never done it, but I think the bolt holes in the cylinder need slotted to fit the bolt pattern of the 044 case. If you aren't very comfortable working on saws, I wouldn't try it because I wouldn't do it without carefully checking piston skirt to crankcase fit and also piston squish height.
Also, be careful as to how old the 044 that you have is. The early designs had a 10mm piston pin, and the later ones were 12mm. If it's the 10mm, neither the BB or OEM 460 parts will fit.
Serial numbers after X29382283 should have the 12mm piston pin.