Here's some information from a hi fi history that dates the first two way speakers to 1931: "The early Western Electric theater systems were of one-way design consisting of large re-entrant type exponential horns. The Western Electric 555 driver was used with these large assemblies. Frequency response was band limited, and the range covered was probably no more than 100 Hz to about 5,000 Hz. Later on, Western Electric added a high-frequency unit as well as an array of low-frequency woofers to augment these systems. They used Jensen 18" woofers in open-back enclosures to supplement low frequencies and a device known as the Bostwick tweeter to extend the upper range. These additions to the basic one-way system appeared in 1931".
But this takes the term "woofer" for granted and does not specify whether the Western Electric engineers called their drivers "woofers" and "tweeters", or whether those terms appeared later. Looks like I don't get the dollar.