Can Li-ion and NiMH Battery Packs Coexist Safely in Bicycle Lighting Systems?

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DocToxyn
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Disclaimer: Forgive me if I phrase these questions poorly, I'm new to electronics.

I am looking into a lighting system for my bicycle which would include something along the lines of a dual halogen bulb set-up powered by either a NiMh (http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=7180509374&rd=1&sspagename=STRK%3AMEWA%3AIT&rd=1 ) battery pack. Besides the weight issue, the Li ion is about half the weight, are there any other advantages (or disadvantages) to the Li ion pack?

Also, I would like to include some LEDs on the bike as "running lights" to enable cars to see me better at night. The manufacturer of the Li ion battery states that other light systems should not be used with that particular set-up, but does nont make this claim for NiMh kits that they sell. I think Li ion batteries have a greater chance of explosion is used improperly, would this be a possibility if I powered maybe http://cgi.ebay.com/ebaymotors/ws/eBayISAPI.dll?ViewItem&rd=1,1&item=4573369618&sspagename=STRK%3AMEWA%3AIT along with the halogen bulbs? The LEDs are rated for use between 6 and 18 V and are pre-wired with resistors and 26g wire, so I think they should work. If they would indeed work, what would be the best way to hook them in with the existing lighting unit? If I haven't provided enough info, please let me know. Thanks.
 
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The danger of exploding Li ion batteries from what I've read comes from recharging them with improper chargers. You'll need to look for a charger that says it's specifically for Li ion batteries or battery packs. The only other way I'd see them burning up is by drawing so much current across them that it's the equivalent of a dead short (but that would pretty much burn up any battery).
 
"...I would like to include some LEDs on the bike as "running lights" to enable cars to see me better at night..."

I looked at the LEDs on your ebay link. I think you should consider something else. In order to use them as "running LIghts" you need some kind of lensing to spread their beams a little.