Considering that fleas don't live on HAIR they live on skin & sucking blood, I don't see how shaving a cat would be very effective
Also a 16 year old cat that is already quite sickly, has numerous medical conditions and probably has never been shaved before.. that seems like a very effective way to kill a cat if anything. Even a totally hairless pet can get fleas... shaving doesn't do a thing to eliminate them, it just makes less hiding places for them, but even then you'd have to shave the cat head to toe to remove all the hiding places, and that is a good way to send the cat into shock. Even pets with little to no hair like a Chinese Crested or the Sphynx kitten I am fostering can get fleas in the right conditions..
To the OP, manually removing the fleas can help too
If your kitty will let you, use a fine tooth comb to remove the fleas and then flush them down the toilet. Very effective. I have only had fleas in my house twice before- once when I FIRST got my cat Socks about 5 or 6 years ago, and a quick application of Frontline got rid of those.. since then only once did I accidentally bring fleas home on a foster kitten and I guess it was towards the end of the effectiveness of their flea stuff and a few of my cats picked up a couple fleas. Quickly applied Frontline again and flea combed everyone adn it was all good.