With one of our oldies we spent her last few days doing literally anything she wanted, when she wanted.
Trundle outside, ok, 4am, whatever - slice of cream cake, have at it - cheeseburger, steak, chocolate biscuits... go for it.
Obviously don't make them feel any more poorly than they already are... but all the things they've wanted in life that they can't have as we know its bad for them... the time for those things is now.
If your old lad is worried by going in the vets, ask if they can do it in the boot of your car (assuming suitable car of course) or back seat as this may be less stressful for him, particularly if he likes car trips. Take him on a big blanket so they can gently wrap him up afterwards to go to the crem or so that you can take him home to sort that part out yourselves.
Finally - not aimed at you OP...
The cruel shaming talk of 'you must stay with your pet when they are PTS' is horrid and its damaging.
If you're able to stay calm and steady, and not distress your pet further, and you want to be there, then yes, be there.
However if you're losing your grip and you're deeply upset or horribly anxious, frightened etc etc, then you're very likely to make your pet more frightened and upset too.
They do not know what is going on - only YOU know.
For them, the process is no different to going to the vets and being anaesthetised - a process next to NO owner is ever present for, nor is any owner expected to be, nor are owners berated and shamed for not being there for that.
If it's not cruel to let the vet put your dog under a GA for an op without you there, then it is not cruel to let them euthanise your dog without you there.
This horrible shaming shit actively puts people OFF euthanising their pet at the right time because they can't face it and they fear asking for help or asking for someone else to be there, and that means animals suffering long past when they should have been let go!