If I were in your situation...
I'd equip it NOW with a BCR. Sounds like you have had positive experience as such with your first PS1 engine. Go with what you know.
I have nearly a dozen PS1's, all with BCRs, all running perfectly (Enough sounds for my satisfaction.)
One engine on this topic I reference to inquiries such as yours. I had acquired a Dealer Appreciation package in the late 90's...featuring a Big Boy with PS1. For reasons that add nothing to this response, I had never run the engine since its purchase. In 2021 I decided to finish equipping all the rest of my PS1 engines...including the Big Boy. It was a safe assumption that the original battery had no charge left, confirmed after I had removed it from the tender. I installed the BCR, put the engine on the track for the first time, powered up to just slightly less than 10v...lights and sounds all came on as expected. Let it sit powered for a few minutes, Reset the throttle,...and away we went!! All functions running perfectly.
I have no experience with a fresh 9v battery as your photo shows. I'll leave response to that choice to someone who has tried it.
And, how long would you be able to run before switching to a BCR?? Why risk it? ASAP! A BCR is your best 'final answer'...IMHO, of course. (Others may disagree)
Just this man's opinion/experience.