I have a Loyal Products made in Taiwan fan with melted 4 wire capacitor. The capacitor has blue wire in and red 4uF, white 4.5uF and yellow 5uF wires out. This is connected to a two layer switch by the red and yellow wire. The white capacitor wire connects to a red wire going into the motor.
My question is: Should I attempt to use a single value capacitor so that the fan only runs at high speed, thus allowing me to use a remote control switching unit?

It's probably easier to replace it with the same value capacitor than to figure out how you would wire a single capacitor and what value it would be (probably 4uf). You can still use a remote control.

Yes, that would be easiest, however I don't know why the capacitor over heated at the blue wire site. Should I expect to replace the switch as well in case that was some how the cause? I will try to add its picture

I don't think the switch would cause it. Are you using the fan with a dimmer switch or speed control?