Re: Rechargeable batteries ... are desinged to deliver high current over a short period.
Rechargeable PP3s come with several voltage ratings. If the equipment really needs 9 volts then you have to make sure that is what you are buying. Some are only specified as low as 7.2 volts viz 6x1.2v cells. The next is 8.4v (7 cells) then 9.6v (8 cells). The offered capacity ratings also vary considerably in the range 150 to 300mah.
For a smoke alarm you should get the ones with the low self-discharge rates. In such superior AA/AAA cells the performance is rated as something like 15% loss per 12 months - so presumably the same for PP3 ones. A standard Ni-Mh apparently has that same loss in only 1 month.
Ni-Mh PP3 recharging is also a tricky area. Many multi-type chargers do not sense "full charge" for PP3 - even if they do so for various 1.2v battery sizes. You have to charge for only a prescribed time - like 12 hours. Overcharging seriously affects the life of the battery.
You can get dedicated PP3 chargers - often for multiple units simultaneously - that are faster and also sense when fully charged. They tend to be relatively expensive.