It will work but an ancient CD player won't have much life left in it and won't sound nearly as good as a modern CD player. Digital audio tech has progressed vastly since 1989.
Marantz and Cambridge Audio have some decent modestly priced CD players. Any DVD/BD player that has analog audio outputs would be another option.
Your choice of new cassette decks is pretty limited. I think Teac/Tascam has some decent models still available but most anything else you find will be pretty low end.
If you want to get a used cassette get one that has had all the rubber parts recently replaced that will be more likely to last a while. Getting parts for some decks can be a big problem.