Many variables here, the legal aspect being a considerable factor, but I would say that you certainly have a duty of care in what is an emotive and complex issue.
Naturally, you want to do the best for your friends, but have you considered:
1) what the passenger's needs may be during the flight?
2) would it just be you and him? if not, is the aircraft big enough for anyone accompanying him to render any medical assistance when airborne? <consider that if anything did happen - how long would it take to get to the nearest suitably equipped airport? Longer than you'd think.>
3) could you cope with the major distraction of such assistance was being rendered so close to you and fly the aircraft? Come to that, could you fly to your normal high standards knowing that your passenger was so ill, even if nothing was happening?
You've made a very laudable gesture, but this is a specialist type of trip, probably best left to those who do it for a living. Most scheduled and charter airlines can make arrangements for such passengers on routine trips and they're better equipped if anything does go wrong.
I'm sure the family would understand and not think anything less of you if you explain this to them.
Hope it all goes well.