I have a friend who works at a homeless shelter, where she and the
other staff have a bunch of keys which they have to keep safe and not
lose (any person who does lose them is personally liable for the cost
of fitting $1000 of new locks).

So I was thinking - does there exist for sale anywhere online a sort
of improved version of the keyrings that beeped when you whistled in
their vicinity, that were popular gifts in the '80s. It would need to
be a much louder "siren" than these ever had, and ideally be
triggered by some kind of radio control that could be kept by every
staff member in a handbag/pocket or whatever.

(I know you can still buy these kind of "whistle-and-it-beeps"
things, and that's not what I want. Also, the shelter will not
do the obvious sensible thing and install electronic locks.)

Hello -

Please note: This question is not finished until you're satisfied with
it.  If you choose to rate this answer, I ask that you do so *after*
asking for any necessary information/clarification or additional
products.

For the following products, you might want to explore www.froogle.com
to find the best price.

Besides a keychain alarm [a list of these are found below], you may
want to explore a pager setup.  You'd have a pager as a keyring/chain
and you'd be able to call it from any phone.  Although I haven't been
able to find a key-specific pager, something like this might work:

Compage 100MF
http://www.sld.co.uk/products/comms/compage.htm

Nixxo Tutti pager
http://www.pagermall.com/nixxo3.htm


Keychain Alarms
================

Key Alert Personal Keyring Alarm - $14.97
http://www.preparedness.com/keyalperkeya.html
Instant Protection. Completely legal protection device can help
dissuade would-be assailants with ultra-loud 120db siren by attracting
the last thing they want attention! Simply push the activating button
with for an ear-piercing, blood-curdling 120 DB blast of sound,
summoning help and encouraging the would be assailant to retreat.
Built in flashlight can also protect property.

KeyRinger
http://keyringer.com/lost-keys.html
Our sonic Key Finder ends hours of hopeless searching for your lost
keys. To use this key locator to find lost keys, simply click the find
button on any other KeyRinger device. The missing KeyRinger responds
immediately with a loud distinctive tone and a bright flashing light.
Anyone can use the KeyRinger to find missing items in just seconds.
Never again be late for work, for school or for an important
appointment.

Dual Locating System
http://store.yahoo.com/dnbenteprisesinc/rt3310.html
Finderz Keyperz is initially sold in pairs and are matched to find
each other. To locate, simply pull out the built-in antenna, press the
finder button on the remote and the extra-loud one-minute beeper will
begin to sound making finding keys quick and easy. The powerful 100’
extended operating range lets Finderz Keyperz operate through nearly
all walls, doors, furniture and clothing.

Now You can find it!
http://www.sharperimage.com/us/en/catalog/productview.jhtml;sessionid=KTQ2WQ1D2FIADQFIA2TCJ0Q?pid=42739300&http%3A//www.sharperimage.com/us/en/catalog/productview.jhtml%3Fpid=42739300&source=17587&_requestid=28966
Includes four beeper discs to attach to keys, glasses and other
elusive objects. Press a button on the portable base and the
corresponding disc beeps loudly. Each disc attaches with keyring or
double-sided adhesive pad.
Effective range of 30 feet. Includes magnetic mounting bracket for
base.
One-year warranty. 


Search Strategies: Google/Froogle.com
=====================================
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Your last suggestion was pretty-much what I was looking for. Cheers.

The first products of this company probably won't arrive for another
year, but they might ultimatly be what you're looking for:

"Steve Wozniak, the guy who brought us the personal computer, has
another idea.
His new company has created a wireless network that he says can help
you find almost anything -- lost keys, lost dog, lost child. His Los
Gatos company -- Wheels of Zeus (WOZ, get it?) -- has designed tags
that you can attach to a child, a dog or just about anything. A
handheld monitor uses global-positioning-system satellites to show
where the tagged items are.
The genius behind the idea, called wOzNet, is in the use of a
low-power, long-range wireless protocol that operates at about 1,200
baud. That's roughly a fifth the speed of a dial-up modem, but fast
enough to send a quick burst of information about an object's
location."
http://www.siliconvalley.com/mld/siliconvalley/6349353.htm