Suppose you have a worksheet called "Settings" which contains a named cell "VBA.ConnectionString" which contains your connection string. Then this code should do the trick (not tested):
Sub UpdateConnections()
Dim sConn As String
Dim oSh As Worksheet
Dim oLo As ListObject
Dim oQ As QueryTable
sConn = ThisWorkbook.Worksheets("Settings").Range("VBA.ConnectionString").Value
For Each oSh In Worksheets
For Each oQ In oSh.QueryTables
oQ.Connection = sConn
Next
For Each oLo In oSh.ListObjects
oLo.QueryTable.Connection = sConn
Next
Next
End Sub