Nevertheless, I would recommend that the circuit should be made in safer way and in a better enclosure (Perhaps a 3DP one – then battery contacts can be taken from a discarded 9V battery or a 9V ...

Five-pack of 9V battery snap connectors (~$2, part #270-325) Twenty four-pack (single pack) of 22-26 gauge wire butt connectors (part #64-3073) 9V battery.

It's true that a lithium 9-volt battery will probably last longer than an alkaline 9V (which in turn should last longer than a carbon-zinc 9V). But how much longer depends on a smoke alarm's power ...