Someone can correct me here if I am wrong, but DCC RPG has gone out of their way to eliminate the 'skill' portion of d20 SRD. People are trying to add back in skills to the game, but I believe that is not what Joseph (and company) are trying to do here.
That being said, I do realize that some tactile / combat related skills seem to be required by some people on the boards. But before we go and try to add back the skill system, lets look at it this way.
I might borrow a few terms from other versions of DnD, so please do not shoot me.

There are basically three types of 'skill' checks in DCC RPG.
1. Class/Racial Abilities/Skills - This are where the class has a strong bonus or affinity for the check. This include racial halfling abilities for stealth
2. Background Skills - Skills related to your characters background. (i.e. hunter could be allowed to do 'survival', 'move silent', but not 'hide in shadows' skill checks)
3. Untrained
The issue you run into is to not poach on the Thief's territory by having a warrior that is stealthy. You could argue that a background of cut-purse could entitle him to those checks. But at what bonus? If the bonus is too high, you are encroaching on the Thief's territory.
I would not be adverse to allowing someone that falls into the Background Skills category to get a +1/level bonus to their DC check.
Untrained would get a straight up check.
From looking at the charts, it would give provide a sizable bonus to the Background skilled people and still allow the class people to excel in those areas.
Note... not all class abilities should be allowed to be used outside of the class.
I do agree that the the term skills should be removed, but I like the term Actions in its place. Because you are rolling an Action Die + bonus to see if you are successful.
This leads to a change in the text in the classes section like this:
Enhanced Class Abilities:
Thief has the following enhanced actions, please see the attached chart.
A halfling would have an enhance ability section of: Stealth (see chart)
etc...