I do feel for you, we have a dog approaching his 17th birthday, and we are well aware that even though he is trundling on now, happy, plays with toys, sleeps a lot, loves his food, is currently 98% continent...
Every day could be his last.
I have to say if he had a visible tumour that was likely to interfere with his arse/willy/eyes/nose/ears/movement... we'd be into 'one smashing last day' territory.
Yes, there are further investigations, there are treatments that can prolong life - but those will also damage quality of life.
Pain meds can cause stomach problems and constipation.
Many cancer meds will cause nausea and stop them eating, which then becomes a battle to address.
Tests are painful, disruptive, stressful, likely to involve being in a strange place away from you, with unfamiliar people.
I do think the vet could have been more diplomatic, however having been on the other side of things in advising people on what to do with their dogs - often people don't hear what you're saying.
So when you kindly tell someone they should give their dog a last great day then book them in for euthanasia, they hear 'we can carry on...' When you tell them that its better to let their dog go now, before they're in significant pain.. they hear 'my dogs not in pain'.
Chances are very high your dog IS in pain - dogs do not show chronic pain all that willingly or easily and many of the symptoms are not things we easily recognise as pain (eg - digging, often a result of stomach/gut pain. Biting paws - joint pain further up they cannot reach etc etc). A dog in their late teens is a dog who already lives with some degree of pain, in the same way a human in their 90s does.
By all means, seek a second opinion on how long and what to expect but please don't subject your lovely dog to a barrage of tests and scans and biopsies and medication. Let them go before they're really suffering, and please... do NOT listen to the old trope 'they'll tell you when they're ready' because its often utter bullshit, many dogs will keep on going because they adore you and don't want you to see them give up, and 'that look' is in my experience, pain, fatigue, discomfort. Give them the gift of letting them go before that.