The title most likely explains everything, I am pretty sure Asset Delivery would be the only web based API to obtain the assets.
But what I am looking for is getting the returned asset file, in an obj format - I can’t use Roblox studio in any way in this for Exporting in OBJ since I want to do it in a web server.
I know how to get the asset from the AssetDelivery API, but not sure how I would request it in a different format.
Roblox doesn’t store assets as OBJ. They have their own file format. There is a few versions of it so you will have to write (or find someone to write) an exporter to obj.