Hide some of the Autofilter arrows using VBA

Some advise on the best way to hide Autofilter arrows for several columns is needed!
Sorry if any of this has been resolved before, but I haven’t been able to find something that works for me (i.e. I have found some codes, but some I could not get to work).

I have included a sample sheet that mimics the setup of my file. I am using Excel 2003.

I want to be able to only show Autofilter arrows for columns B, C, D and I
I have created a module with the following macro:

Sub Hide_Dropdown()
With Range("A8:N8")
.Autofilter field:=1, Visibledropdown:=False
.Autofilter field:=2, Visibledropdown:=True
.Autofilter field:=3, Visibledropdown:=True
.Autofilter field:=4, Visibledropdown:=True
.Autofilter field:=5, Visibledropdown:=False
.Autofilter field:=6, Visibledropdown:=False
.Autofilter field:=7, Visibledropdown:=False
.Autofilter field:=8, Visibledropdown:=False
.Autofilter field:=9, Visibledropdown:=True
.Autofilter field:=10, Visibledropdown:=False
.Autofilter field:=11, Visibledropdown:=False
.Autofilter field:=12, Visibledropdown:=False
.Autofilter field:=13, Visibledropdown:=False
.Autofilter field:=14, Visibledropdown:=False
End With
End Sub

Is this the best thing? It means I have to run the macro for all sheets, which I don’t mind doing, as long as it remains like this when I share the spread sheet and others open it. I have not had it confirmed whether this is indeed the case by other users - if it is then it is probably fine to leave this as it is.
Or is it better to have a macro like this that runs automatically when the worksheet is accessed?

The worksheet is protected with p/w “test”

Thanks