"Instead of the pat-down, you can always request to pat down your own scarf, including head and neck area"...

Two facts should be self-evident to demonstrate how outrageous this idea is. First, the whole point of being searched by someone else is to find concealed objects. A "self-pat-down" clearly defeats that purpose and is a completely unacceptable lapse in security. Let's remember the stakes here: if something goes wrong in air security in the wrong place at the wrong time, people die. There is enough margin for error in the system already without adding this variable.
Secondly, the fact that Napolitano could even be considering such a measure highlights a double standard for special treatment that would not be considered for any other religious group, but is extended to Muslims without a second thought. What is going on here is a politically correct sort of anti-profiling: by all appearances, the air security apparatus bends over backwards to profile Muslims as not being a threat, in a way that it does not strive to reassure other demographic groups in the traveling public.
We are told time and again that Muslims in America just want to be treated like everyone else. Ergo, if you want equal treatment as a Muslim woman, participate in your social responsibilities equally even when it is awkward or inconvenient, rather than acting like some kind of demigoddess whose head and neck are untouchable by sullied human hands in the screening line. Your head and neck are as human as that of the next non-Muslim lady in line who is no more thrilled to be there than you are.
But let's remember why we're standing there waiting with our shoes in a plastic bin, and why so many security procedures have come into being in the first place: Islamic jihadists keep trying to bring down our planes, more and more with explosives concealed on their bodies.
"Napolitano considering allowing Muslim women to pat themselves down at Airports!" by Jack Minor for the Greeley Gazette, November 17 (thanks to C.):

With the holidays fast approaching, the Transportation Safety Agency has announced new security procedures requiring passengers selected for secondary screening to go through a machine that produces a full body scan producing a nude but grainy, black and white image. Passengers choosing to opt out of the scan will face a full body pat.

The problems these security measures pose should be discussed in the interest of the entire traveling public, pilots, and flight attendants, and not as the problem of one group.

The head of Homeland Security has indicated the government is considering the request of an Islamic organization that has suggested Muslim women be allowed to pat themselves down during a full body search that is part of new enhanced procedures at airports.

Since implementing the procedures, numerous complaints have arisen that the search is not a "pat-down" but rather feeling and grabbing along a person's genitalia and other areas until they meet resistance. Critics have said the pat-downs would be considered sexual assault if performed elsewhere.

The TSA defends the procedures as necessary in light of last years "underwear bomber" and the recent issues involving printer cartridges being used in an attempt to blow up cargo planes.

The Council on American-Islamic Relations, CAIR, has expressed concern with the TSA over the regulations and recommended special procedures for dealing with Muslim women. The organization issued a travel advisory for Muslims over the procedure.

In the advisory CAIR advises all Muslims to contact them and file a complaint with the TSA if they experience any "disturbing incidents" with the new procedures and they feel they have been unfairly singled out for screening.

It goes on to make special recommendations for Muslim women wearing a hijab covering their face. The advisory says women are to inform the officer they are only to pat down the head and neck and says "They should not subject you to a full-body or partial body pat-down." They also recommend that women should be permitted to pat themselves down and "have the officers perform a chemical swipe of your hands."

Barack Obama's Homeland Security Czar, Janet Napolitano, is considering changes to the procedures to address the issues raised by CAIR....