I'll see if I can find the UTube video on Peradon snooker cues for you.
Lots of work with a hand plane. Not sure if they use a lathe or not for some parts.
There is one video where a guy makes a Snooker cue by hand. The end result is ok for a home built project but nothing that you would want to take to the hall with you.
Mind you, with a little practice, the guy might get better at it.
The Peradon video that I watched before showed them doing a lot more hand planing, even the shaft work.
I have a ton of respect for precision machinists and what they can do with a cue, but really, I could do just about all of the basic work of making a cue by hand if I had to. Maybe not working in tenths, but tolerances of 1-2 thou can be achieved by lots of practice and careful observation. The eye is incredibly accurate if trained in a systematic fashion. Most guys using machines won't get there because they don't need to. They have they machines and indicators (and, of course, their knowledge) to do that part for them, so their eye never gets "in" like a hand worker's eye gets.
It wouldn't take an incredible amount of time, either, nor would it have to be prohibitively expensive. The hand-planed snooker cues you mention are proof of this.
I have made more than a couple of the do-hickeys in the photo below. This one I made over 20 years ago, and it is still straight as an arrow is spite of years of play while in tension from the tightened hair.
They take 2-3 days to complete (how long does a Plain Jane take to make?) The work is done almost entirely by eye, with a minimum of fixtures and only a couple measurements as a starting guide. A few templates are usually used, but they aren't really necessary. A machine lathe is used to make the sterling silver adjuster button, but only to cut those two little decorative rings. The facets on the adjuster are hand-filed by eye. With a bit of practice a file and a good eye can get spectacular results.
Thousands of makers over the last two centuries have used the same basic techniques. They work, so no need to create elaborate machines to fix what ain't broke.
Bottom line is that if you have a machining background, the first thing you think when you see a cue is a machine lathe. If you grew up using fine hand tools, you'll be thinking planes, knives, spokeshaves, files... and lots and lots of sighting.