We need to replace the thermostat in an old mobile home. There are two wires, though the current thermostat does work heat and cool. You switch over from heat to cool on the unit itself. Do we need a heat only thermostat?

It the switch for heat and cooling on the furnace. Does it say Heat-Off-Cool and it is a rocker type switch ? If so then

Y to W terminals will be used in homes where the heat/cool mode is selected at the furnace and not the stat. This would usually cause heat and cool to be on at the same time but in your case you use the Y and W terminals on the replacement thermostat since the actual change over is happening at the furnace switch.

You will need to stick with a very simple thermostat since there will be no power robbing available because you only have two wires. If the new thermostat you get has batterys make sure you always have spares on hand.