Many of the coolest asymmetric designs are electric watches but there are quite a few mechanical and automatic models as well.
One example of a mechanical asymmetric is the 1960 Sea Ranger. Although the crystal and dial is oval shaped, the top of the watch is a differently shaped than the bottom of the watch.
Produced from 1960 through 1962, the Sea Ranger came with Hamilton's 12/0 sized, 22 jewel 770 movement under the hood. It's actually a fairly large watch. The "weather proof" aspects of the watch come from the case design and gasketed crown. The two piece case opens from the front and the stem is a two-piece design.
I've only had one example and I tried to change the crystal in it three times. The crystal appears to be press fit into the bezel and after cracking three crystals I finally gave up and put the old one back in.
It's a sharp looking watch and collecting all of the mechanical asymmetric models would be a fun but expensive challenge.