“Enough power” is not the issue. If we ignore the efficiency of the transducer itself, the electrical power in is the acoustic power coming out.
What a too-high load impedance does is it doesn't draw enough current to produce the output power that the source is capable of. On the other hand, a too-low impedance draws too much current, resulting in audio distortion or damage to the source.
Whether or not the specifications you have say so, in practice there must be a range of acceptable impedances. 4 Ω and 8 Ω are common full-size speaker impedances and they can be considered fairly low. Headphones can have a very wide range of impedances, commonly 25 to 600 Ω, but in general higher than typical speaker impedances.
Additionally, simply for acoustic reasons, headphones/headsets/earpieces always need much less power than a speaker, in the sense of something that you don't hold directly to your ear, requires. Thus, a particularly high impedance is not necessarily a bad thing.
All this together means that it is highly likely that an output that says it can drive an 8 Ω speaker will almost certainly be just fine — possibly even too loud! — when used with a 44 Ω transducer.
If you hook it up and it turns out it doesn't work well, and you confirm that it is for impedance reasons, then the solution is to use a transformer with a suitable ratio and frequency response.