David Wexler started out in the early 1920's as a salesman for Targ & Dinner. Some time after 1930 he left to start his own instrument distribution company a couple of blocks up for T&D but still on Wabash St. in Chicago. The company is still going today as a musical instrument distributor but some time in the latter part of the 20th Century they moved to Arizona and are sometimes called Wexler Music Co. Currently I can see no Ukuleles in their catalogue. 

While still in Chicago they registered a number of brand names like Whitehall, Cortini and King David for use on other instruments but the two I have seen used on Ukuleles, (and Guitars), are Wabash, (registered in the early 30's), and Conrad, (registered in the late 30's). All of the Ukuleles I have seen with these brand names were produced post WWII, starting with Regal as the OEM but soon moving to far eastern imports. Both brands had Sopranos and Baritones but I've never seen any other sizes. What there was though was at one point in the 50's they marketed a very distinctive box shaped Soprano.