The "W" (Watts) rating of a resistor is the maximum power it is capable of dissipating. The data sheet for the TP4056 does not give the internal circuit so it is not possible to work out the actual power dissipated in the resistor. As the supply to the circuit is 5 volts then the maximum power that would be dissipated in a 27K resistor would be if it had the full 5 volts across it. Even if this was the case there would be just under 1 mW dissipated. So any resistor you could buy would be able to dissipate this amount of power. I think 1/8 Watt (125 mW) are the smallest resistors I have seen.
I would check that the resistor does give the correct charging current as it is only an assumption that scaling the resistor value outside the given values is valid.
Les.