It seems like in Ken Burns documentary there is like no mention of pilots carrying weapons. Did they not carry weapons at all in the cockpit in case they had to bail out over enemy territory where in all likelihood they would be taken prisoner otherwise?
I mean even astronauts cosmonauts nowadays with the Kazakhstan Space Program carry shotguns in case they have to crash land in the middle of nowhere to fend off wild animals.
For reference: Footage of Everett Alvarez from the preview of the "Vietnam War" by Ken Burns
Yes, pilots had sidearms. S&W M10 and M15, chambered in .38 Special, were the normal issued sidearms. 1911A1's were also available as an option to some. Exactly what was issued depended on the branch, when they were serving, and what they were flying. Pilots often carried personal weapons. Many did prefer using revolvers, due to their simplicity and reliability in adverse conditions. Those who did use personal weapons did often use something chambered in .357 Magnum, so that a little extra "oomph" could be had, but it still was able to make use of .38 Special (which is same diameter, just shorter length).
Also, it wasn't unheard of for planes to have CARs (Shortened M16s) for the crew to use. This was standard practice on O-1 Bird Dog and O-2 Skymaster spotting planes. On helicopters, of course the M60s that were used by the door gunners were also removable to be used after abandoning the craft. Ithaca M6 Aircrew Survival Weapons were also included for pilots in case they needed to forage for food. The M6 was a double barrel, with one barrel chambered in .22 Hornet, and the second barrel was for shooting .410 shotgun shells.
Sources: http://www.flightjournal.com/iconic-firepower-aircrew-sidearms/
"US Helicopter Pilot in Vietnam" By Gordon L. Rottman, Osprey Publishing.