You
don't need a driver if you don't want the magic smoke to remain in your laser diode for more than, say, a few seconds.
All electronic devices are imbued with a small quantity of magic smoke at the factory. That's what makes them tick. Let the smoke out, and the stop working. 
The LM317 CC driver that
Fretwrecker94 linked is one of the easiest things you could build. If you're game, you can even build the whole assembly onto the back of a diode. It's not something I'd really want to try, but it has been done before.
On the other hand, if you
don't want to fiddle around soldering bits and bobs to stripboard, might I recommend these
nice, dirt cheap linear drivers from AixiZ.
They do 80-500mA full range and to set the current you just need to tweak the pot while watching the current readout. They're incredibly easy to use.
If someone hasn't already suggested you a diode, I'd recommend
this thing. 20mW of 635 at the manufacturer's recommended current and voltage.
$17 isn't overly expensive either (for a single-mode 635nm diode).
The
really awesome thing about 635nm is that beam visibility is at least on par with 445nm. It's not quite 532nm-visible, but it's a
major improvement over 658nm. Most of the guys over at the 'lexicon use a ratio of 1:1 between 532:635 when they're shooting for a nice white (with additional blue, of course).
If you're in a dark (or even semi-dark) room, 15-20mW of 635nm should be more than easily visible.
The other thing to take into account is the angle from which the observers will view the beam. A beam is significantly less visible when viewed transversely (that's a word?) than if one were, say, looking down it. Try it for yourself. Stand behind your laser and look down the beam. Then try moving yourself around relative to the beam and watch how the visibility changes.
Now, speaking of darkness, there's several things you can do to make the beam more visible without turning up the power.
If the venue has dimmable lights, use them. You've said it's a prop, so I'm assuming it'd be for some sort of production or whatnot.
And of course, use some sort of particulate in the air. And I say particulate because I don't necessarily mean it
has to be fog. If that's the case, using a fogger (fog machine) would be entirely inappropriate unless you could fog up the entire room and let it disperse slowly. Because foggers aren't exactly known for a nice, even production rate. They
fart a dense cloud of smoke for a little while and then stop. So one moment you'd have a room with nearly nothing in the air, and the next, nobody can see a thing.
Foggers don't exactly have the best hangtime either; you're looking at around 10 or so minutes in a small room and less than 5 in an air-conditioned room. If you do it right, fog can be very discreet, yet bring out a beam like nothing else. If you do it wrong, you'll have everyone choking one minute and nothing left the next.
And if it
is a production, sudden bursts of fog may or may not be appropriate (cue disappearing stage). If you have a budget of some sort, I'd recommend going out to your local music store or sound/vision/lighting store and hiring a hazer. They work like
this. Not a lot of fog, but a steady trickle of it instead. Great for filling up rooms slowly (and keeping them filled). Just about nobody notices them (which is always nice). You also don't get the sudden disruptive BLAAAAAAAAAAARP of glycerine vapour leaving a nozzle at high pressure.
Over here on the other side of the pond I can get one out for around $80 a night (and these are high-quality Martin units).
I'm guessing you have a fog machine. Canned smoke isn't exactly a viable option for a large-scale rig (for a desktop optics table, it'd be fine, but for anything bigger, don't even
think about it). Canned smoke has
no hangtime, the propellant is flammable, and often it smells nasty as well.
Now, if you can't get a hazer, but have to use a fog machine instead, you can always see if your machine has an 'idle' or 'standby' mode. Normally when they're idling, they let out a gentle trickle of fog or a very small burst every few seconds. Send this through a fan, and you have an instant hazer. It's far from ideal, but it'd be much better than using a fog machine in burst mode.
A 1kW fogger on continuous burst can do horrible things in a 24sqm room. #LFMF.
But still -- your best option would be a 635nm diode and a fogger. (Relatively) inert (not eye-safe, of course, but
much safer to handle than a 658nm DVD burner build) , relatively easy to build too. Worst case scenario it'd be a little
too bright in conjunction with the fog, in which case you could back off on the diode current or the fog density.
Anyway -- I hope all of that made some sense. I did a tour of duty ( :/ ) as a lighting tech a while back and hopefully what I've dumped into this post is of some help to you.
Questions? Give me a buzz. I don't bite; I promise.
