There are significant differences in safety between the lithium battery types. Lithium Iron Phosphate (LiFePO4) cells are considerably safer than the ones traditionally called 'lithium-ion' (particularly lithium-cobalt, often used for cell phones or laptops). One manufacturer even drove nails through their cells to demonstrate they wouldn't erupt in flames like a Li-Ion could.
Not saying they aren't a potential hazard, any time you have that much energy concentrated in a small package you have to be sure it doesn't get loose.
I'd be fine using LiFePO4 in my yak, though I'd definitely be taking it out for charging - but then I don't charge any removable battery inside the devices anymore, even AA NiMHs. I would want to be sure the LiFePO4 battery had a proper cell balancing circuit inside, or use an external balancing charger, though. The Battery Tender battery listed doesn't mention what sort of cell balancing they use.
Battery University has a chart of safety vs capacity for the various lithium types and what they are used for:
http://batteryuniversity.com/learn/arti ... ithium_ion