No, if you want to use the Twitter API you have to use oAuth.
First you have to create an App, don’t worry about the callback URL much, just leave it blank (if this is possible) or enter some dummy URL there, you won’t need it if you want to use Application Auth using a bearer token. Alternatively you could, after creating the App, request tokens on your behalf and just use these. (This is probably easier, depending if you oAuth library or whatever you are going to use is capable of doing App only auth)