Corrie, I think Jasper's point is that some insurers (we are also with Nationwide) will still insure you for most things but not for a recent diagnosis for which treatment isn't complete.
I don't know about lymphoma, but we have certainly accepted that arrangement for my prostate cancer while I was awaiting treatment or during it. Talking to the doctors there was little risk of any emergency situation arising during our trip.
Both Thailand and Singapore have (private) medical systems as good as most places in the world, as you say there is the slight risk you might have to bear the cost but if your husband is essentially fit that is small. If you have the "rainy day" fund* to cover the worst case scenario I would go. It is a time to make the most of the health you have and build memories.
[*To be fair, according to the news Thailand has suffered from too many rainy days recently but I hope things will settle down there by next month. We had a memorable holiday in Thailand earlier in the summer, and I hope you do too].