The album came out in 1957—Waikiki is lettering, not a typeface.
The general style is sometimes referred to as Bounce or Jazz Latin. Similar digital typefaces (to greater and lesser degrees):
P22 Daddy-O Blackface
Western Egg & Avenue
House Industries Latino
Eddie Fisher Bold
Ravenwood
Crazy Loot
Horsefeathers Bold
Roquette
Stand Up JLN
Risque Pro
Fontdinerdotcom Jazz Dark
MardiPary AOE
Thingamajig
Able Press
Harry Plotter
Perfect Magic
MVB Hotsy Totsy