Among some people, the idea of a skill system is a controversial one. If you are a hard core OD&D player I guess that attitude makes sense. I grew up on MERP and BRP derivatives, so for me the existence of skills are natural. I see how the idea of skills can be limiting for the players, giving the intention you have to have a skill to try something out. Maybe they can be used in another way.
The thing is, if you always rely on the game mechanics to role play, you can use skills in another way. Having skills be fairly broad, they can be an indication of how to act or behave. Say that you have the skill "Play the Lute". Can you play the flute? On the other hand, if you have a skill like "Perform" or maybe even "Bard", you can take that as an indication you posses a cluster of knowledge you can use to build a personality around. Maybe skills, broadly sketched, are best used as a basis for roleplaying, not for rollplaying. I hope you catch my drift here?
In Tunnels & Trolls 7th ed. there are Talents. They are like skills, but you only have one as a starting character and I've seen them more like a kind of mechanical support for roleplaying, not mainly as a way to gain a bonus for when you roll dice. Maybe that attitude could be used in other old school games?