Not sure, combining HTML and Flash is in general what I try to avoid the most.
Now in your case it would be mainly a matter of testing it.
Do like any HTML testing, focus on the big browsers like Chrome, Firefox, MS Edge, etc.
try to have a serie of steps to follow, either to provide to people if you need to test under different OS,
or ideally install/setup VM to test it yourself.
Even if someone were telling me "oh yeah wmode work exactly like that", I would test it for myself no matter what
Most of the time you will get hearsay from other people, and in my experience especially from devs
"oh no you can't do that, I already tried", and other "I'm telling you it is like that", etc.
it is always by ignoring those that I learned and achieved the most
I have heard that wmode transparent and wmode opaque are slower
Who are the sources? is it some qualified engineers at Adobe ?
Unless some guy took the time and effort to really test it with repeatable tests, samples, stats etc.
do the work, test it yourself, only way to be sure
Maybe it is slow only if you try to layout HTML over a software rendered video or vector animation with a lot of alphas, if there is no animations or it is only text maybe the "slowness" is not that obvious, depends a lot on what you try to do.
Note: I'm not saying to not trust other devs, I'm just saying that I see often devs who don't even try to do something because they heard some other devs who told them it was not feasible.