Sending few commands with BLE without microcontroller
The module already includes a microcontroller. The website you linked to says:


  The on-chip processor has sufficient space for many applications, so a carrier board may only include sensors and a battery. The module is based on a Nordic nRF52832 chip that has an ARM Cortex-M4F, which includes 512Kbytes of flash memory and 64Kbytes of RAM.


You'll need to write some code for it in order to convert your contact closures into appropriate messages, but the only additional hardware you'll need is a power source, the switches and possibly some pullup resistors.