Unfortunately no, as Nintendo DS is too weak to run any form of Half-Life engine. Doom is available though and there is a "fanmade" WAD of Half-Life for it, which would be the closest thing to run Half-Life on DS.
You can check one of Steam downgrading guides (available by Googling), but I'd advise to install a new Steam (you need to find a 8.1 compatible install first) into another directory and try to see if it works that way.
Is this Half-Life itself or another mod? Because the engine is hardcoded to hide singleplayer maps only if the game name matches with one of those:
Half-Life
Opposing Force
I had to name my Half-Life Deathmatch (because plugins break the singleplayer) "Half-Life" just to avoid the singleplayer maps being shown up in the list and keeping them in valve folder.