Endless.com is one of the shoe-shopping websites that allows you to browse just by those shoes labeled as "vegetarian". At the moment, it is showing 26 pages of vegetarian shoes (at 40 per page). Although this doubtless includes strappy sandles, sneakers, clogs and other footwear that isn't quite office-appropriate, that still leaves quite a selection from which to choose.
Unfortunately, you cannot cross-search by style, vegetarian is an alternative search to "pump" and "flat". However, you can further narrow your search by size, width, heel height, brand, price, and even color family.
Although I am not certain of their algorithm, it appears as it takes more than just being leather-free to make the cut. For example, a shoe with a manmade sole and satin (silk?) upper is not appearing on the vegetarian search engine. The same is true of a pair of shoes with "fabric" upper that appear to be made of wool. My conclusion is based on the fact that other shoes from the same maker do appear in the search, and the assumption that the shoe manufacturer does the labeling, since the system is by no means complete. For example, a pair of rubber sandles with no animal content fails to appear in the search.
Yet although one looking for each and every leather-free (or vegan) shoe on the site might have to do their own work, the fact remains that this is a good resource as is. Importantly, it is one of the places currently liquidating the Te Casan by Natalie Portman line of shoes, a line I have raved about for its comfort and quality.