I disagree with barkingdog here.
Although accidents happen all the time, careful, responsible people have less accidents. I see no issue with trying to habituate a clawless cat to travel....but you have to be UBER-careful because can escape. That said... Life is a terminal disease for everything that lives and calculated risks are necessary or life gets really boring or we become too paranoid.
A boarded cat at a vet is safer, but way more traumatic for the average cat. If we are thinking about the cat's best interest, imo, it isn't being boarded at a vet's for who knows how long and at what expense.
A Cat in a locked cat carrier, for me, is like Zero risk if the people around that carrier won't open it. If you have young kids, another story.
It goes without saying that the cat needs to be wearing a collar 100% of the time and that the cat should 100% be microchipped. It goes without saying that you'll want to know exactly where a recommended vet is in the new town you will be staying at. You might also mention this to your current vet for suggestions and/or possible anxiety reducing medications.
To get the cat into the carrier with less fuss turn THE CAGE UPWARDS so that the open door faces the ceiling. Then lower the cat inside the carrier back paws first.
I'd start with very short trips. maybe just bring the cat to the car the first time. Then back home - and the cat gets treats. Maybe the time after that drive around the block. then back home then the cat gets treats. Keep increasing the time until the cat feels comfortable. But know that some cats may never feel comfortable...