WOULD AN AC/DC TRANSFORMER DAMAGE THE FLASHGUN LONG-TERM?

I have a portable pro flash gun (Toshiba ES-38L) which is powered by 6
AA batteries arranged in series. The voltage across the positive and
negative terminals is therefore 9 volts.

It eats up batteries and I would like to use it indoors with an AC/DC
transformer.

I have such a transformer, a variable voltage output that includes a 9
volt setting. It gives a REGULATED supply, it is rated 1400mAh.

I have tried the flash unit with the transformer already and it
worked, but the sound it made was different. When it powers up using
the AA batteries the sound the flashgun makes is smoother (more of a
pure whine).

My question is this, WOULD THE TRANSFORMER CAUSE ANY LONG TERM DAMAGE
TO THE UNIT?

(I noticed that it charges well with the transformer set at 6 volts
too, should I leave it at 6 volts?)