Is there any way to hide your Steam status from others?

Open your friends list and change your status to Offline, and that should be what you need. You can't do it for specific friends, but if you're just trying to play solo that will do the trick.

Click "add non-steam game" then add something like notepad. You can then rename it whatever you want to make it less suspicious. Run it from steam and it will show you as in a non-steam game called whatever you decide to name it. Then run the game you actually want to play and your status will remain in the non-steam "game" you launched first.

Edit: As of 2018-04-10 there is a built-in setting to hide your currently played game in Profile > Edit Profile > My Privacy Settings > Game details. Set this to Private, but take note of the other profile items affected by this setting. Since it would hide so much of your profile, this old answer may still be useful:

You can maintain a "blue" online status while playing a Steam game.

This method requires multiple instances of Steam. For example, sign into the same Steam account on 2 different machines. Set your status to Offline in the instance you'll play your game from, and set the other instance's status to whatever you want your friends to see.