Air carrier Captain reported the company transport procedures of battery powered mobility devices are inadequate. Reporter requested additional guidance for flight crews.

Narrative

During the boarding process I was made aware of a mobility scooter to be loaded onto the aircraft. I proceeded to ask what sort of battery was installed in the device and whether it could be removed; which I was advised it was not able to be easily removed and was of a lithium variety. It's been my understanding that we are not able to take any sort of lithium battery in our Cargo Hold and that the battery would have to travel in a cabin. I contacted the On-Call Pilot who advised he would get in touch with Person A to provide further guidance and clarification. Whilst waiting for the return phone-call; I devised a plan to take the wheelchair in its stowed position in the crew bag closet. This seemed to be the best option at the time as it satisfied my understanding that the lithium battery had to travel in the cabin with us.On-Call Pilot and Person A returned my call and advised that we are able to take such a device in the cargo hold provided it met certain criteria. I was not provided any details of the device specifically during the boarding process nor was I notified if it met all the criteria written in our Dangerous Goods Manual. Having found a solution myself; I communicated this to both Person A and On-Call Pilot and continued the flight.Having had the time to read the DG Manual; I'm not entirely sure whether I was actually able to take such device as I did not verify it met: Regulations: DGPM XX-XX.X.X.X; 1.d 'The lithium ion battery must be of a type that successfully passed each test in the Company manual of tests and criteria as specified in 49 CFR XXX.XXX unless approved by the DOT Associate Administrator.'DGPM XX-XX.X.X.X; 1.e'e. Medium and large lithium-metal batteries are forbidden aboard a passenger carrying aircraft.'DGPM XX-XX.X.X.Y'Medium and large lithium-ion or lithium polymer batteries are those which exceed 25 grams of equivalent lithium content or have a capacity rating over 100 watt-hours.The information provided to myself as PIC (Pilot in Command) did not confirm or deny any of the above references; only that the device had previously traveled on Company the day of our departure; and other previous flights.I understand that I may have a misunderstanding or a lack of knowledge in this area and made the decisions based on my commitment to safety. I would like to see further guidance on the carriage of these devices in either our manual and or a crew memo.