you wrote "I was un-aware the the civil Tiroler used airguns, so far my impression, and looking at contemporary pictures - the usual flint lock rifle was used."
One of the keys to this is the knowledge of the artist. The artist knows flint lock rifle and what they look like, so, that is what they draw. The artist does not know airguns, so, they are not drawn. It's about impossible for an artist to draw something that they are not aware of.
There are of course so many pictures and drawings of 1809 conflict but these are almost universally drawings based on, or building upon, the nationalist myths surrounding the conflict.
The knowledge of Tyrollean manufacture and use of airguns is mostly from inference. The Austrian Model 1780 "Girandoni" Repeater airgun was handmade by Bartholomaus Girandoni who was born and raised in Cortina d’Ampezzo. It was Joseph II who approved of Girandoni's design and moved him from Cortina to Vienna to make the airguns for his army. So, we can be sure, that prior to 1780 airguns -powerful pneumatic airguns fully capable of hunting- were made in Cortina. Bonaventure Lacedelli was another Cortina gunmaker known to have made airguns. As I've stated, not much else is known, as there are virtually no known examples of these early airguns, just as there are very few Tyrol firearms from the period - they were all destroyed. There is also a significant amount of literature that talks of the Tyrollean's and their airguns but these are all casual mentions without any description. Finding a proper contemporary description of an airgun is extremely rare; just like artists, writers cannot properly describe things that they do not understand.
Note: Vienna circa 1820-1830 was a hotbed of high quality airgun manufacturing; Johann Contriner, whose work often carried the k.k. supplier makings, being one of the most famous.
One of the things about airgun history is that there are few real facts and many myths that have developed over time. Tracking down the origins of these myths has proved to be an interesting challenge. It's also interesting that the greater challenge is disproving these myths to the airgun history audience (a small group, for sure) because the myths are more appealing and are well supported in the modern literature. For instance, http://en.wikipedia.org/wiki/Girandoni_air_rifle , the gun seen here is indeed a Girandoni type of airgun but it was not made by Girandoni, wasn't even made in Austria, this particular type of airgun was made in England. The people who own these airguns get very angry at any mention of this. Fighting myths with facts is not always an easy thing to do.