Three things.
- You need antennas IF you use Wireless on the Ax3, in theory if you disable the radios you don’t need the antennas at all BUT in practice it is wise to disable the radios AND put a couple of dummy loads on the antenna connectors (or - alternatively - very short rubber ducky ones turned horizontally), so that should the radios be accidentally enabled there won’t be any problem, see:
http://forum.mikrotik.com/t/hap-ax3-other-antennas/174477/1 - The WAF (or SOAP) is very relevant here, would the Ax lite be acceptable? (if it is actually fast enough for your use)
https://mikrotik.com/product/hap_ax_lite
See:
http://forum.mikrotik.com/t/hap-ax-lite-vs-hex-750gr3/171771/1 - About PoE powering the Audience through another Mikrotik device with PoE out port is not “mandatory”, you can use any PoE power supply/injector with Mode B passsive output, since it will be a short distance a 24V one will be fine.
Another possible approach could be to re-use (with dummy loads) your existing Ax3 and get a L009 for the home office?