Yes an HVLP paint sprayer would work well. Even a regular cup gun would be fine if you have the compressor for it. Remember all of these types of sprayers apply a fairly thin coat at a time so it could take more time to complete the project. But you will have great control over how much is applied and the spray pattern.
If you decide to use an airless choose or purchase a small tip, 210 or 211. More over-spray than an HVLP but overall faster.