There are plenty of workarounds, connection via a smartphone or computer via youtube or other such as streaming platforms.
I had more than 9500/10000 titles and unfortunately it’s often the same titles that come back and therefore I did some sorting!
But I always stock them on a medium just in case and I obviously regularly renew the titles and they are all classified by genre, then artist and best in relation to the years of release.
Currently I still have 8000 titles left but if we prepare an evening correctly with 200/300 in case that is more than enough, especially when the interviews with my clients are precise in terms of their musical tastes with a list of titles which are essential to them and which allows to know their musical styles and I also ask them the titles or artist or see kind not to pass in the evening as a blacklist.
For each evening I provide a personalized form for the event that simplifies the evening and yet I do not work at all with playlists, I just learn to know my customers and also their guests with relevant and useful questions.
Everyone has their own way of preparing their evenings!
Exfat ! 
Same with USB key, SSD internal or external…: