they should take a 'hot-desk' laminate from reception when vacant and put it on their desk
Instead of going elsewhere to get a sign, keep a sign at every desk.
For visibility, make it a toy-sized flag in a stand or something else vertical.
When someone sits, they take down the flag.
When the person departs, they raise the flag.
When we're not in the office, we leave a sign that says "This desk is available for hot-desking". I don't think you need anything else than that.
If you want to be more specific, mention when you'll be back.
Sounds like hot-desking is a short term band-aid here.
If your office is "rammed", then soon(er or later) you will need a larger office. Perhaps try concentrating on that?
If not feasible, I would recommend allowing more working from home.
But it sounds like management has their head in the sand over this one.
[Update, after your comment] Personally, I ...
I worked in several companies, and there were plenty of times when someone needed to sit for some time (from a few minutes, to a few days): candidates for jobs, people in business trips, ...
There was never any process about it. Someone (insider) would spot a potentially available desk, and ask around if the regular "owner" is using it during that day or ...
In our office, we have the policy of every desk is free to use. But IF you know you come back tomorrow MORNING, then you can leave your stuff there (Mainly Keyboard, because everything else is put away).
When you know you are absent the next day, put your keyboard somewhere else, like a locker or put it behind the screens or something. If the space before ...
We have tried making colleagues aware that they should take a 'hot-desk' laminate from reception when vacant and put it on their desk. This didn't work as wanted as people either didn't comply, or the signage wasn't obvious enough among the sea of desks.
You're doing it the wrong way around.
You're putting a flag on a "free" table.
What you should do is ...
Why not make the desks available by default? Change the culture so that when you come in in the morning you can sit at any desk that is free.
This way you maximally use the available space. People won't avoid empty desks because 'Bob usually sits there and he might still come in.' If Bob comes in later, he'll take the next free desk.
This does require you ...
Perhaps put a label on everyone's usual desk with their email.
When the desk seems vacant for a while, people can email to ask if the occupant is out of the office.
They'll either get an out-of-office response, meaning yes, or if the person is just away for an afternoon and didn't set one, they can always quickly respond yes/no.
For those where the ...
My suggestion is to assign the job of maintaining the signs for desks to other people.
The people who use the desk already have a lot on their minds - they can very easily forget to set the flag. Or they might have to rush out and not have the time. Or some might indeed "conveniently forget", too. At any rate, it's exctremely error prone, as you've already ...