Women specific design isn't really women specific. It's short torso long leg design. Most "men's" bikes are designed for a longer torso and shorter legs. There are men who ride WSD bikes, and there are women who are best off on a "men's" bike. If your arms are much shorter than your height, that's an indicator that WSD might be better for you... but it's not foolproof.

I'd find a shop that will let you do test rides and I'd try several of each. One of the bikes should stand out as fitting better. Tiny hands means you want shifters and brakes that are easy to reach. That's usually fairly adjustable.

Oh, and a road bike won't automatically make climbing easier. I'd look at the gearing on your current bike with Sheldon Brown's gear calculator. Then when you find the road bike that you think is "the one", compare the gearing on the two bikes. If the road bike doesn't have low gears that are as low or lower than your current bike's, it won't be better on hills. The bike shop should be able to swap parts if "the one" has gearing that's really really off. Long term, the only way to make climbing hills easier is to climb more hills .