Programs written for DX 8.1 will run under DX 9 just fine, provided the developers did their job and properly queried for the presence of features before invoking them. If not, all bets are off and you may get weird behavior.
Hope it works out. DX9 was the last release to maintain backward compatibility with previous versions, which is probably why Win7 dropped support for older versions. DX10 and beyond are stand alone releases, so if you have a DX10 program you can't get away with only having DX11 installed.