MP2733 with constant current source

Hello, I plan to use a MP2733 to power a 12V LED and charge a single Li-ion cell.
It would be powered by a constant current source of 500mA. Would it be okay or should I use a buck/boost charger such as the MP2760 to get a constant voltage ?

What is the voltage of your constant current source? My feeling is no, not a good choice. It is a fine charger of a single cell battery but I don’t see where the 12V LED fits into the picture, unless you can put that on the input side.

The source voltage matches the load to give 500mA. When connected to the LED it gives a little less than 12V. The thing is I don’t know how much the voltage will vary when connected to the charger and its cell.
The LED would be powered by the charger itself (maybe through a boost converter if the charger can’t output enough voltage) since it’s a power path charger.

In that case the diodes are acting as a shunt voltage regulator. What is the voltage of the current source in the event it is unloaded? My concern is that that voltage is high and would blow up any IC that it powers.