You are right, new batteries come with a charge of about 50-75% from the factory, and for maximum lifetime they should be operated between 20% and 90% charging state, and should ideally be kept between 10-30°C.
I work in automotive future technologies and the industry learned a lot about battery technologies. We are talking about battery lifetime of 500.000 to 1.000.000 km now, AFTER the industry learned that it's crucial to keep the battery within that temperature also during storage. This was really a learning effect over the past years, and now electric cars have heating and cooling active all the time to keep batteries in that temperature range, also when parking.
A single full discharge at low current should not have any measurable impact on lifetime or capacity.
I'd fully charge it, then connect some headphones and set it shuffle and let it play.
After 10 hours it should be around 20% +/-, then you know you are ok.
As a nice side-effect you are burning in the player