Run-time error '1004': Microsoft Excel cannot paste the data

Question

I have looked up the question and have seen several solutions addressing things like Select or having protected worksheets, none of which apply to me here.

For various

Answer 1

Just wanted to let everyone know I have found a (sort of) solution. Based on the answers/comments from Tim Williams and PeterT I modified the code to look like this:

Sub CopyAllShapes()
Dim ws As Worksheet

' Sets the non-generated worksheets as an array
nSheets = Array("EXAMPLE", "Weekly Totals", "Menu")

' Copies the Picture from the EXAMPLE sheet to all worksheets not in the array and then assigns a 
' seperate Macro called "Export" to the picture on each of these sheets.
For Each ws In ActiveWorkbook.Worksheets
    If Not IsNumeric(Application.Match(ws.Name, nSheets,0)) Then
        Sheets("EXAMPLE").Shapes("Picture 1").Copy
    On Error Resume Next
        ws.Range("J62").PasteSpecial
    On Error Goto 0
        ws.Shapes("Picture 1").OnAction = "Export"
    End If
Next ws

Application.CutCopyMode = xlCopy
End Sub

This has successfully ignored the error and everything is working properly now! Thanks everyone for your help, hopefully this aids someone else in the future!