14500 vs 18650 charge circuit
The schematic for that module is here: https://www.waveshare.com/w/upload/d/d2/Solar_Power_Manager_Schematic.pdf
I admit I'm a little concerned looking at it. I only spent two or three minutes looking over the design, but:

The schematic in general looks pretty sloppy, it's pretty clear that the designer was new to Altium (for example: M1 is a dual MOSFET, but has been drawn as a box)
The designer has specified a maximum power point tracking (MPPT) chip (Consonance CN3791) but has not connected it properly. As per the datasheet, the MPPT pin should be fed by a divider from the solar supply, but instead it is grounded through a 10k resistor. This means the MPPT feature won't work.
The designer has, for some reason, placed an LED and resistor directly in parallel with the battery. Thus, even if the battery protection trips, this LED will still be connected to the battery and continue to draw current. Left for long enough, this could over-discharge and permanently kill the cell.

Anyway, yes, you can use this circuit with a 14500. Depending on the recommended charge rate of the 14500 you may need to change the series resistor, though. R1 and R3 in parallel set the charge current. Their equivalent value is 0.11 ohms, so as per the CN3791 datasheet, the charge current is set at about 1.1 amps (\$I_{CH} = \frac{120 mV}{R_{CS}}\$).
The typical 14500 has somewhere in the neighbourhood of 1000 mAh capacity, and the usual recommendation for most lithium ion batteries is to charge at 0.5C max or around 500 mA (consult your specific cell datasheet to confirm). I'd suggest depopulating either R1 or R3, which would set the shunt resistance to 0.22 ohms and thus your charge current to about 550 mA.
EDIT: Sorry, I guess I misread your question. I just saw that this is the reverse case, this charger is designed for a 14500 and you want to use it with an 18650. In that case, yes, you can go ahead and do so without modification (other than the battery holder). I would not change the shunt resistance at all, since around an amp is pretty much perfect for the typical 18650. I'm surprised they are marketing it as a 14500 charger with an 1100 mA (~1C) charge current, that seems a bit irresponsible.