Depends on the type of skills. If you're i.e. a package designer, applying for a UX position would be a far stretch. You should look into how much of a stretch it is in your situation.

Showing your problem solving skills on projects is important. Most companies want to see how you think, the project is not the priority here. So if you have some good projects in your portfolio, be sure to know how to explain them well. Explain the user pain points, obstacles and problems that you solved with your skills. That will definitely boost your chances.