Sensor data transmission without using a microcontroller?
The only remotely sensible solution is to use an MCU.

That was true last week when someone asked a remarkably similar question, 
and it remains true today.

MCUs are cheaper and more flexible than all but the simplest combinations of building block logic, and have the added benefit of drastically expanding the sorts of radios and radio protocols which you can consider, letting you add checksums or cryptographic security, letting you go to low power modes in between readings, letting you build in self-test diagnostics, readily tag transmissions with a unique ID, even giving you the option of storing sensor calibration in the device rather than a database...

An MCU would also typically make the PCB layout easier rather than harder, because at least if your layout and firmware people are on speaking terms, you can often put functions on any one of a number of pins in order to make the layout simple; conversely with building block logic or special function ICs you often have to use one particular pin without a choice.