Here's the instruction on how to integrate Twilio with the shortening service to send bulk SMS that contain short links. https://short.cm/support/Connected%20Apps%20&%20Services/zapier-twilio/
my bad, missed the part about a 3rd party thing, and seriously, chill on the whole shady thing, i was just giving you crap.
Anyway i googled: https://short.cm/pricing They have a free option, sounds like a fit.