Three Points-
1- In the Hospital, his SURGEON is the Doctor in Charge
2- It's NOT likely that the Hospital will trust / accept a patient provided instrument for monitoring and dosing. It's a legal (and medical) thing. THEY are responsible for his care and outcome and will only trust THEIR established tests / instruments.
As one Coumadin Clinic Nurse told me long ago, she had NO problem with me having a Home Tester, but told me that she would have to make her recommenditions from THEIR tester (Coaguchek) or Lab Draw.
Sorry About That.
That said, you could always ASK, but don't count on a positive response.
3- As a Heart Patient, he is going to have to learn to come to grips with needles, IV's, and other invasive stuff. That's just the way it is. Hopefully you can get some help on how to achieve this from his Doctors and/or Nurses, maybe even a Psychologist.
FWIW, I always ask for a Butterfly Needle which is quite small. If your son has prominent veins in his hands, that may be less 'uncomfortable' than 'digging around' in his arms.
Tell him to either Close his Eyes or Look Away.
Also suggest that he can 'grit his teeth' or tighten any OTHER muscle, but to let the 'target area' go LIMP.
I learned that lesson as a child after tightening my leg muscle before getting a Booster Shot. It was SORE for a WEEK!
Good Luck.
'AL Capshaw'