You can instruct Poodll to never show Flash audio and video recorders. To do that go to the Poodll filter general settings:

Site administration -> Plugins -> Filters -> Poodll -> General settings

And there remove Red5 and FlashAudio from the preferred recorder order settings for each recording type. 
It will probably look like this:


In cases where HTML5 recording is not available the user will only have the option to upload a file from their PC.