Danger, Will Robinson, danger! Open carry, accidental or not, except for some limited outdoor recreation exceptions, is not explicitly permitted under Washington state law. Doing so, especially in urban or suburban areas, will rapidly draw the attention of law enforcement. And here is the statute that they will use to charge you:
RCW 9.41.270
Weapons apparently capable of producing bodily harm — Unlawful carrying or handling — Penalty — Exceptions.
(1) It shall be unlawful for any person to carry, exhibit, display, or draw any firearm, dagger, sword, knife or other cutting or stabbing instrument, club, or any other weapon apparently capable of producing bodily harm, in a manner, under circumstances, and at a time and place that either manifests an intent to intimidate another or that warrants alarm for the safety of other persons.
(2) Any person violating the provisions of subsection (1) above shall be guilty of a gross misdemeanor. If any person is convicted of a violation of subsection (1) of this section, the person shall lose his or her concealed pistol license, if any. The court shall send notice of the revocation to the department of licensing, and the city, town, or county which issued the license.
(3) Subsection (1) of this section shall not apply to or affect the following:
(a) Any act committed by a person while in his or her place of abode or fixed place of business;
(b) Any person who by virtue of his or her office or public employment is vested by law with a duty to preserve public safety, maintain public order, or to make arrests for offenses, while in the performance of such duty;
(c) Any person acting for the purpose of protecting himself or herself against the use of presently threatened unlawful force by another, or for the purpose of protecting another against the use of such unlawful force by a third person;
(d) Any person making or assisting in making a lawful arrest for the commission of a felony; or
(e) Any person engaged in military activities sponsored by the federal or state governments.
There have been countless successful prosecutions, especially in western Washington, under this law for open carry. Living in Snohomish county as I do, and having the occasional interaction with local law enforcement (as part of my job), I will bet cash money that open carry anywhere in this county will get you a quick citation. And if you are foolish enough to open carry in an intimidating manner, you will also have your carry permit revoked. Permanently.
The bottom line is that unless you are engaging in outdoor recreation in a rural area (I am ignoring Federal land here such as National Parks or National Forests), open carry is not explicitly allowed under state law, and doing so exposes you to substantial legal risk.