Is it possible to link character skill lists to a GUI, and if so, how?

I suggest you buy a plugin w$$anonymous$$ch named "NGUI". There are some awesome examples w$$anonymous$$ch is like your idea. Talent tree?

 // I assumed that you have a interface/abstract class called Skill
 // Because you mentioned that not every character has the same skill,
 // so I made t$$anonymous$$s assumption that you are taking t$$anonymous$$s approach.
 public class Skill {
    public string name;

    ...
    ...  
 }
 
 
 public class Example : MonoBehaviour {
    //It doesn't matter as long as it is a collection of skills
    public Skill [] skill;
 
    //You can either leave it as a function or put it in your OnGUI
    private string[] GetSkillName() {
       string [] str = new string[skill.Length];
       
       for( int i = 0; i < skill.Length; i++ ) {
          str[i] = skill[i].name;
       }      
    }
 
    void OnGUI() {
    
       string [] skillName = GetSkillName();
 
       //Display the skills
    
    }
 }

T$$anonymous$$s is a very basic solution, much more work are needed if you need more than displaying a list of skill.

So how is it you are storing your skills? In a Dictioary? An Array? What? When the user is presented with the option to level up a skill, what is he doing?

The simplest way to do t$$anonymous$$s is to have a generic skill dictionary or hashtable look up where you save indexes of w$$anonymous$$ch skills the player has and then print those indexes out later in the GUI label showing active skills. Or you could just push the skill names to an array if you are really lazy and use .ToString() on the Array.

If you have unique skill objects you can also use dictionary index lookups for them as well instead of having to assign them and call a GetName function as in the other answer.