This isn't what you wanted exactly (it's not a fix for the original game), but there is a free, 99.9% accurate port of Blood to Windows, via the eDuke32 game engine (a Windows port of the Duke Nukem 3D engine), and it's fantastic. It has proper mouse support, fully configurable controls, support for high resolutions, etc, so is much more convenient to use than the DOS game Blood.
Just download BloodCM_v02.2016.zip from:
http://m210.duke4.net/index.php/files
You don't even need any files from Blood, everything is in the zip file.
The only disadvantages are that it doesn't (yet?) support fan made mods/levels, or the later official expansion packs.