IF you're going for 14" for "safety", then I'd recommend you stick to the 13"s. There's not much difference in 'safety' going up by an inch. The breadth of the tires count - that's the contact surface.
Your skidding is more likely caused by worn tires than smaller rim size. And remember, going up an inch means having thinner tires, so the overall diameter is still the same. You would have changed nothing (except your bank balance)
My personal opinion: Change to 13-inch tires with better threads. I'd say something in the range of Conti CC's or Yoko C-Drives.

Wow... times have changes a lot. I'm getting old I guess
The last set I got were Michelin Certis. NEVER regret those - the best set my 'ol Saga ever had (and still has). They were RM135/pc when I bought them in 2010. Maybe the thread starter can still get them?