I use the small microfibre towels. They‘re a bit like a window leather and when damp, absorb an amazing amount of water. When Humphrey‘s really wet I can rub over and just keep squeezing them out. Afterwards I just rinse them through and pop them back in the plastic box so that they stay damp. Ive still got the original one I bought over four years ago, but have bought a couple more since as spares and then throw them all in the machine every now and again to freshen them up. The advantage is that they don‘t need drying.
I bought mine on Amazon here in Germany but have seen them in UK, I think there are various makes but they all work on the same principal.
Only other suggestion would be a doggy hairdryer /blaster - I bought one (also on Amazon) fairly cheaply and its been a Godsend.
After having had to wash smelly woolen socks for 40 years, which had been worn in firebrigade boots during a 24 hour shift in the middle of summer , my OH wouldn‘t DARE challenge smelly dog towels in the washing machine!!