Yes, I am certain all melee weapons use strength, and all ranged weapons use dex. We ran some tests years ago. That's why crossbows and dex based swords have such high base damage. They have to make up for the low damage from stats (if you use crossbows you have high strength and low dex, whereas if you use dex based swords you have high dex and low strength).
Also, the master sword is by far the better sword in my opinion. It's fantastic for dex users. It can be used to easily bridge certain gaps in terms of mastery, such as 50 -> 60 to earn the master combo without burning 20 skill points, or even 90 - 100 where you can save even more points. If you are a dex user, you are likely to spend a lot of points on bows (or you might as well go strength), so saving points on melee skills is very nice indeed.
Edit: Also, it's very easy to both get and use master swords and rapiers. They're at 60 and 50 dex respectively, which is very easy to get compared to the whooping 110 that Betty requires. By the time you get 110 dex, you will most likely have the Claw of Beliar.