Is it possible to hide first person blood stains in Black Mesa Source

Just keep going. The crowbar is a little bit later in Black Mesa than it was in the original Half-Life, but it's impossible to miss it and it's not that far away. It's pretty linear at the beginning, so just go whichever way is available until you get it.

Black Mesa is a fan made total conversion mod of HL2, recreating the original Half Life. A team of volunteer artists, coders and level designers have painstakingly recreated the beloved HL single player experience, adding vast amounts of new details such as more scenery objects, more detailed landscapes, and richer textures. They even recorded new dialog to freshen that up too.

Half Life: Source was a port by Valve of HL to the Source engine. There was no new content added and the textures werent updated, so the only differences were better lighting, shading, and physics. It looked a bit better, but played the same, and was really only ported as an experiment to test Source's modding capabilities.

In short, HL:S was a better way to experience HL if you'd never played it by the time HL2 arrived. BM is a chance at reliving all the magic again, but in a very new and handcrafted way.