Li-Ion battery charging as simple as possible
Are you familiar with simple modules like this ? It is basically a simple TP4056 board, for sure 1A is too much for you but a simple exchange of a resistor fixes that.

Although the suggested pulse charging to 4 V will work without doubt and I also think that that is a method that is safe enough. If you need to make the pulse and compare voltage then maybe a TP4056 (or any other similar IC) will be less complicated. The IC takes care of everything so you don't have to :-) And for the price, I know what I would choose.