Dave Peterson wrote:
I think that person B will have to answer the prompt.

Why do you think that?

I finally overcame my relunctance to experiment with the link feature
myself, and in fact, I discovered that it works exactly the way I
expected. My conclusion: There is no reason why Person A cannot email
a workbook that does not prompt for "update links?" and does not
attempt to update linked data.

It really is very simple. The creator of the workbook, Person A,
probably wants the following option set: Edit Links Startup Prompt
Let Users Choose to Display the Alert or Not. Then whether or not Person A sees a prompt depends on the setting of the option Tools Options Edit Ask to Update Automatic Links.

When Person A prepares Workbook 1 to be emailed to Person B, Person A
can set the option Edit Links Startup Prompt Don't Display the
Alert and Don't Update Automatic Links, the Save As another file name.
It is the saved file that Person A emails to Person B. Note that this
does not alter the options in Workbook 1. This ensures that the
Workbook 1 update options remain consistent with Person A's wishes, yet
the emailed workbook meets with Person B's needs (viz. no prompt and no
update).

Of course, it might be ideal if someone (moi!) provided an add-in macro
for Person A to use to facilitate this procedure. But Person A is a
more-sophisticated Excel user than Person B. I can expect him to
follow the multistep procedure.

Dave Peterson wrote earlier:
I don't know why your "startup prompt" option is greyed out.

Presumably because the spreadsheet (or workbook) that I tried this in
initially did not have any linked data. (Klunk!) Apparently, Excel is
clever enough to make this Edit menu item available (not grayed out)
only when there are linked data.

(FYI, I wrote "the Links is grayed out[; i]n other words, I cannot
click on the Edit Link item". I did not say that the Startup Prompt
option was grayed out.)