The law regarding knives in the District of Columbia is DC ST § 22-4514b:
"No person shall within the District of Columbia possess, with intent to use unlawfully against another, an imitation pistol, or a dagger, dirk, razor, stiletto, or
knife with a blade longer than 3 inches, or other dangerous weapon."
(
http://government.westlaw.com/linkedslice/default.asp?SP=DCC-1000)
In theory, perhaps, that permits carrying such a blade
without "intent to use [it] unlawfuly against another," but I am not an attorney and cannot verify that theory.
If you plan on entering Federal buildings the relevant law is 18 USC Sec. 930:
"(a) Except as provided in subsection (d), whoever knowingly possesses or causes to be present a firearm or other
dangerous weapon in a Federal facility (other than a Federal court facility), or attempts to do so, shall be fined under this title or imprisoned not more than 1 year, or both....
(g) As used in this section:...
(2) The term "dangerous weapon" means a weapon, device, instrument, material, or substance, animate or inanimate, that is used for, or is readily capable of, causing death or serious bodily injury, except that
such term does not include a pocket knife with a blade of less than 2 1/2 inches in length."
(
http://uscode.house.gov/search/criteria.shtml)
Buildings such as the White House and the Capitol Building (and its associated facilities) have their own more restrictive rules about what can be brought in. No knives are allowed.
As far as museums are concerned, many, if not all, Smithsonian museums
will allow knives. The Hirshhorn Museum, the National Portrait Gallery/American Art Museum, the Renwick Gallery, and the National Zoo allow knives and do not have metal detectors. The Natural History Museum has metal detectors, but usually does not operate them and, when it does, still ordinarily allows <2.5" knives. I do not know what the Air and Space Museum currently allows (they have both allowed and not allowed knives in the past). The National Gallery of Art and the Spy Museum, not Smithsonian museums, both allow knives and lack metal detectors.