So it is no longer any skill check of their choice - the caster has to indicate the specific skill to buff.  But it no longer says the spell ends after it is first used, so it lasts for any checks for that skill for a minute? 

It's a good trade off imo. This balances Guidance while keeping the utility. I knew a guy who basically told his DM "assume I am casting guidance every minute" just so he could always have it. My friend would at least have to specify the skill lmao

I appreciate the "Choose a skill" it makes the guiding feel more intentional and thematic with your "guidance"

Nice. You can guide someone to be Stealthy and they get a full minute of being stealthier. Or more Persuasive, etc. I like it.