D&D 5E A maladroit rogue?

[Sword of Spirit]

It seems to me like it would work. Your AC is going to start out as good as a Dex rogue, and if you wear a breastplate once you can afford it your AC will only max out 1 point lower than a Dex rogue. If you take expertise in stealth you'll only be 1 point behind a Dex rogue (and you are wearing a chain shirt, so same AC as Dex rogue, and no Stealth disadvantage) to start. The Dex rogue is going to max out with a +17 Dex mod, and a minimum result of 27. You would max out with a +14 mod and a minimum result of 24. I'm not sure how often you're ever going to need more Stealth than that.

So the AC difference is 0-1, and the Stealth difference is 1-4 points (and it hardly matters at the levels its greatest).

IMO, that is absolutely worth it. You'll have more hp, better Athletics, and all the other dwarvish goodness (including darkvision, which some races lack).

Given all that, I don't see why your mountain dwarf Strength rogue with a 14 Dex can't effectively do any sort of rogue-ing he wants. Even with another Dex rogue in the party, you can leverage your Athletics and hp to show him you aren't inferior.

 

[Spartan_MD]

Thenmatically, it would be nice to use dual hand aces(which are effectively short swords) and light hammers(which are effectively daggers) for sneak attack for your mountain dwarf rogue, but it would violate RAW.

I was toying with this concept with an inquisitive so my cunning action could be used to gain advantage for dual sneak attacks....

 

[Swarmkeeper]

Flavor over optimization almost always makes for more memorable game play, in my experience. You can add DEX as you hit the ASI levels, if you really want/need to. Starting off, you are behind a +1 compared to "optimized" builds, but I agree that's not a big deal. You will still be effective and it is a different build from what others at the table might expect.

For comparison sake, my son plays a Half-Orc Rogue Assassin and he has ended up being one of the party tanks in our CoS campaign due to good constitution, sneak attack, and Relentless Endurance. He's at level 9 now with 17 DEX but just earned that at last ASI (level 8) as he chose instead to buff his INT at level 4 for Investigation purposes.

Have Fun!