Again, I don't want to discourage you. Here's an idea: Allocate part of your practice time each day or week to this song. Start with the first chord. Am is my all time favorite uke chord because a) it's super easy to play, and b) I like minor key songs (like Hotel CA). So practice that chord, and you'll have learned a very useful chord that appears in a lot of beginning uke music. Then work on the next chord: E7. This is also one of my favorite chords because a) it's not too hard--way easier than a regular E, and b) it sounds really good with Am (don't just take my word for it, Don Henley apparently thought so too
).
Then work an playing Am-E7 in rhythm. Hotel CA sounds fine with a simple rapid up-down-up-down-up-down-etc. strum. You can use a more sophisticated strum later. Then sing the first line on top of your Am-E7. Pat yourself on the back. Whether it took minutes, days, or weeks to get here, you are making progress toward playing the song.
Then add in G, D, F, and C (the most common uke chord), then Dm. Each time you add two chords, you'll be able to sing another line. By the time you get to Dm, you'll revisit your friend E7 and you can sing a whole verse.
I think Hotel California is actually a great song for learning these chords as the changes are not complex (half of each stanza is one chord, the other half is another), and when played in Am it uses a lot of useful first position chords.
You won't be able to play along with the record in that key, but you'll be able to play it and if you want sing it just fine on your own.