I'm no expert or "guru" here, but why go the VX route? When they were available, the Civic VX had one of the WORST reps for being a pointless car. That is, not a huge savings in fuel, but a very poor drive as Civics go. The VX into a CX shell would be somewhat similar to installing a VTEC engine in a non-VTEC shell as the VX is somewhat of a VTEC engine...sort of early I-VTEC?
If you want fuel economy, stick with the CX/DX engine (you don't say what year CX, and after '95 the CX was just a stripped DX). I had a '92 CX and my Honda mechanic said the CX's engine had some design flaw (I never got him pinned down on this point) that made them less long-lived than the '92 DX engine. I went with a non-VTEC Integra engine in mine after it seemed to start drinking oil in large amounts and the fuel economy stayed the same or improved somewhat (tho I did have it modded with a CAI and a header/free-flow cat-back exhaust).