How to change the shipment date on change of posting date

Changing the Posting Date will also change the Document Date. Did you have a look at the code in the OnValidate-trigger of the field Posting Date how this is achieved?

PS: be sure that doing it in a similar way for the Shipment Date that calling the OnValidate-trigger of Shipment Date makes sense.

Open table 36 in design mode and search for Posting Date field (field 20). Open C/Al editor (F9) and see the code of the OnValidate-trigger of Posting Date field:

Posting Date - OnValidate()
TestNoSeriesDate(
  "Posting No.","Posting No. Series",
  FIELDCAPTION("Posting No."),FIELDCAPTION("Posting No. Series"));
TestNoSeriesDate(
  "Prepayment No.","Prepayment No. Series",
  FIELDCAPTION("Prepayment No."),FIELDCAPTION("Prepayment No. Series"));
TestNoSeriesDate(
  "Prepmt. Cr. Memo No.","Prepmt. Cr. Memo No. Series",
  FIELDCAPTION("Prepmt. Cr. Memo No."),FIELDCAPTION("Prepmt. Cr. Memo No. Series"));

VALIDATE("Document Date","Posting Date");

IF ("Document Type" IN ["Document Type"::Invoice,"Document Type"::"Credit Memo"]) AND
   NOT ("Posting Date" = xRec."Posting Date")
THEN
  PriceMessageIfSalesLinesExist(FIELDCAPTION("Posting Date"));

IF "Currency Code" <> '' THEN BEGIN
  UpdateCurrencyFactor;
  IF "Currency Factor" <> xRec."Currency Factor" THEN
    ConfirmUpdateCurrencyFactor;
END;