I think that's a good idea as you can ask them about having some Metacam in case he has any pain. It's very common for older hamsters to be on Metacam and it's very easy to give because it tastes nice - a bit like honey. It's the equivalent of Ibuprofen for humans. An anti inflammatory that gives pain relief. Older hamsters get things older humans get too, like arthritis and toothache so it can give them a bit more bounce when they're on pain relief. Ageing is quite sad, but the hamster's spirit is still willing. All the while they are enjoying their food and life generally and still doing normal hamstery things, they have quality of life, and the Metacam just helps that quality of life.
The MSD piece you linked is a veterinary manual so will be quite clinical. However many vets still don't know a lot about hamsters, unless they are an exotic vet. Exotic vets do a lot more training in hamster illnesses. So if you can, when looking up local vets - trying googling exotic vets in your area. Sometimes there is only one exotic vet in the practice for small animals so then you ask for an appointment with that vet. The price is no different. Sometimes there aren't any exotic vets for some distance so then you'd need to go to a general vet, but as long as they are a good vet they will know about Metacam and ageing symptoms in hamsters.
That piece you linked is specifically talking about thrombosis (blood clots), and as Elusive says, what commonly happens with hamsters is it's just wear and tear on the organs as they get older. There are many types of "heart failure" which is a dramatic sounding term but generally just means the heart is having to work a bit harder. Most older hamsters have a degree of kidney failure as well, but they manage fine. They just start drinking and peeing more usually.
I think the way Cookie is, he doesn't seem like he has a critical condition where he could die within a week. He seems like a little old man who is just ageing gracefully.
Having said that, when they do get older, we always have to be prepared that one day they may just pass peacefully. But the best way to look at it is just enjoy every day and hope they carry on for another few months to a year.