MT5 is MT5 whether is is Hedging on Netting! It makes no difference! But the same applies to MT4 as well!
EDIT: OK, I see now you are referring to the Menu options and not to the Chart right-click "Object List" (or Ctrl-B).
So use Ctrl-B or on the Menu use "Charts->Objects-Object List" and then use the "List All" and the select them all (Ctrl-A) and then click "Delete".
PS! Maybe "Delete All" from the menu already does that, but since I have never used it from the menu, I don't know if its the same!
I was not referring to MT4. I specifically answered your question presuming MT5 as I use it too. I just mentioned MT4 because what I described applies to both.
However, it is still uncertain why the trade graphics are being transferred to other charts if you are indeed deleting them before you save the template.
There must be other steps in there that you have not mentioned that could be the cause for your trouble with the graphic objects appearing on the other charts as well.
Are you running an EA on the primary chart? Could it be the cause? Could it be saving to the default template without your knowledge?