Individually create appointments

Is it possible to create a service that isn't on your regular schedule? Where you tailor the appointment time based off of a discussion with the client and send them their own special scheduling link? I do not hold regular hours and schedule appointments verbally based off of day to day availability for individual energy healing sessions.  I use acuity mainly for the yoga class side of my business.  Would it be better to do scheduling for energy healing session in my square account and sync it into my acuity calendar?