I can certainly recommend these:
http://www.ebay.co.uk/itm/Mini-Supe...ing_LightsLanternsTorches&hash=item462cf8a7f8
A bargain and seem to work well with a reasonable flood beam due to the lens. Just tweak the metal terminal if you have any battery contact issues. These are my go to cap lights though I use Photon Freedoms on the 360 mounts too.
You can use a CR2032 (225mAh) in White light Photon Freedoms rather than 2x CR2016 ( 2x 90mAh). The max light output will be lower but they will work fine and you get a longer runtime and value for money as a CR2032 is more than twice the capacity of a CR2016 but you will only pay for one cell, not two.
If you want to convert Photon Freedoms or cheapo key ring lights to use on a cap or other hat then that is simple enough. Get a Neodymium magnet, something like an N50, 15mm and a reasonable thickness such as:
http://www.ebay.co.uk/itm/10pcs-15m...685?pt=LH_DefaultDomain_3&hash=item5662977995
Stick the magnet to the back with a good glue or double sided tape. Avoid the ones with supplied 3M tape, it usually isn't up to the job. I will be using a small blob of Gorilla Glue in the future I think. Super glue would probably be fine.
You can also use a small piece of heat shrink tube to make a slide on cover that holds a bigger magnet and the light together.
Now for the hat. Grab some steel washers or 1p coins. Paint, lacquer, cover in cling film or otherwise protect them from moisture so they don't stain things when they get damp. Drop them inside the sweat band etc of a baseball cap or other hat. Pop the magnet torch into place and adjust to desired position. With strong enough magnets you can hold the lights in place through a hat peak but they work well at the sides on the thinner band near your ears. You could use strips of covered steel in the band to provide easier all direction adjustment. Cheap, effective and magical!
The great thing about sticking Neodymium magnets on the cheap keyring lights that have a lock on function is you can pop them anywhere you can stick a coin or where there is ferrous material, either to light or for storage/emergency.
The other thing I tend to pop on the back end of them is a mini carabiner.
atb