Playford Edition:

‘The Night Piece, or the Shaking of the Sheets’ can be located in the 4^th edition of The [English] Dancing Master. (1670) 

The initial appearance of ‘The Night Peece’ is located in the 1^st edition of The English Dancing Master (1651).

 Documentation Between 1603-167-:

  Information to follow.

Documentation Prior to 1603:

In Act 1; Scene 1, of Thomas Heywood's A Woman Killed with Kindness (written 1603; published 1607) Sir Francis and Sir Charles have the following exchange:

• "Sir Francis: Some music there!  None lead the bride a dance?
  
  Sir Charles: Yes, would she dance 'The Shaking of the Sheets'.  But that's the dance her husband means to lead her." (1)

‘Shaking of the Sheets’ is mentioned in Act 2; Scene 3, in A Pleasant Conceited Comedy; Wherein is Shewed How a Man May Chuse a Good Wife from a Bad.

•  "Brabo: When he comes next, turn him into the streets. Now, come, let's dance the shaking of the sheets."(2)

 There is some debate regarding the publication date of the play.  While the inscription states 1602, the publication year of the first edition states 1605. 

In 1589, John Lyly wrote a short tract called, Pappe with a Hatchet,  where it states:
 

• "Martin tunes his pipe to the lamentable note of Ora whine meg.  O tis his best duance next shaking of the sheetes; but hee good man mean no
  harm by it. ⁽⁵⁾

In 1849, the Shakespeare Society printed Extracts from The Stationers’ Company of Works Entered for Publication Between the Years fo 1570 and 1587.  In September of 1579/1580 the Defence of the Bald Head submitted by H. Denham, wherein it states:

• Some youths that went to France without their haire you meete:
  There they have learnt the merry dance, the shaking of the sheete.⁽³⁾

‘Shaking of the Sheets’ is mentioned in Stephan Gosson’s The School of Abuse, (1577).

• “Domitian suffered playing and dauncing so long in Theaters, that  Paris led the shaking of sheetes with Domitia and Mnester the Trenchmour with Messalina.” ⁽⁴⁾