@Dontgiveup I would not worry as the folks who perform this are trained doctors not technologists. They have contingency plan just in case but it is like a day surgery and they will monitor you about 5 hours after the procedure before they let you go home. You might want to call the hospital to know the procedure details and how you need to prepare for it. They also did blood test to see the clotting factors and kidney function before they schedule this procedure for me.
Regarding C1 shaving & Styloid removal, I have posted a link that talks about the safety and lengthy of hospital stay (My long journey to diagnoses of Jugular Vein Compression by Styloid & C1 - #6 by KoolDude). You are right the swelling takes time to subside and might be the case with that UK patient.