Trigger an alarm with wired smoke detector
It goes without saying you'll want to follow the manufacturer's instructions to the letter, as well as all relevant electrical, fire, and building codes that apply from both a safety perspective and a compliance / legal perspective.  Fire alarms are no place to get creative.
With that said, you may be in luck - if your smoke detectors are compatible with it, Kidde makes a relay module that does exactly what you want:

DESCRIPTION:
This module is only activated by a smoke alarm interconnect signal.
The relay portion of this module can be used to activate auxiliary warning devices such
as external bells and sirens, hallway or stairwell lighting. It provides isolated, (no internal connection to 120 volts AC) normally open, and normally closed contacts.

It should be possible to replace the upstairs smoke detector with this module and a bell or siren.