Do you mean deodorant or antiperspirant?
If antiperspirant, I agree the Mitchum unscented is the cheapest and very effective way to go. I also came across an American brand stick antiperspirant called Almay, which is very good.
But if you shower in the evenings, really, any spray-on 24hr anti perspirant will actually last 24 hours nowadays. Spray it on before you go to bed, and the scent will be gone by the time you get up. The new Clinical Protection antiperspirants like that from Rexona, actually says on the box that it is best applied the night before, and it has no scent by morning.
If you really mean deodorant (i.e. doesn't stop sweating with aluminium salts, just stops the sweat from breaking down and getting smelly) well, you can just use designer deodorant sticks. With a few exceptions (e.g D&G PH) most of them are pretty weak scent-wise, and your edt will overpower them easily.