I don't think you need any special linux distribution. I would just go for the latest ubuntu version, even if it is 64 bit, and see if when it boots it detects a wireless device. I can do that no problem on my HP tablet, which has virtually the same hardware, and UEFI as well. This is not an android tablet with locked bootloader, you can run whatever x86/amd64 linux distribution you want.
Just download it to a USB flash drive using unetbootin or similar, and delect the boot media from windows (keep shift pressed and reboot - you will enter a menu, select troubleshoot, advanced and then boot from the correct drive).