This is not a UITypeEditor issue, but a TypeConverter issue. What you can do is derive from the standard EnumConverter class, like this:

[TypeConverter(typeof(MyEnumConverter))]
public enum TestEnum
{
    a = 1,
    b = 2,
    c = 4
}

public class MyEnumConverter : EnumConverter
{
    public MyEnumConverter(Type type)
        : base(type)
    {
    }

    public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType)
    {
        try
        {
            return base.ConvertTo(context, culture, value, destinationType);
        }
        catch
        {
            if (destinationType == typeof(string))
            {
                // or whatever you see fit
                return "a";
            }
            throw;
        }
    }
}

PS: you can avoid the exception catch and do your own conversion, but it may be more difficult than it looks in the general case (depends on enum underlying type, etc.).