Is it OK to underpower a run capacitor?
Your terminology is a bit off   A 55uf 440v cap Provides a phase shift for the motor so you will not be under powering the cap but the motor.
Will it work with a 45uf?  Probably but start may be a bit harder.
I change caps quite regularly on single phase systems , I try to stay within 10% of the original, if I don’t have one that is within 10% would I use one that is almost 20% under?
Yes I have and it worked until I could get the proper size 3 days later.
I did monitor the start &amp; run currents the system I believe was a 5 ton it was drawing close to max on startup ~35 amps and was taking 2-3 seconds prior to drawing less so I checked it it worked did not draw two much but did not leave them without cooling on a hot day(s).
Having the wrong size will cause the motor to take longer to start drawing more power so you don’t want to do this with a system that short cycles 5 starts per hour no problem from what I have measured but it should be replaced with the proper diced cap soon. The extra draw is not only hard on your motor but on the contactor an electronic switch inside the unit that uses a low voltage to turn on a higher voltage /high current device like the compressor motor or fan.
So it is possible but you should verify the system can get to speed (it usually takes longer) not all systems have the same sizes so without the motor size it is a possibility where I have done this.