Eames Dining Table question  

Faux pas ?
Like, a social faux pas ? It certainly wouldn't be a design mistake, in my view.

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Agree, I think the rubber/hard plastic edge is superior to the veneer edge, which if its applied after the top layer will then chip so much more easily, the proper way to apply it is bottom/edges/top. You can buy the iron on stuff (yuck) but will find it hard to get a match. The rubber edge has a T profile which is vibrated/hammered into a slot with a power tool.
Tell her to relax 🙂

Yeah-- what's the violation/ social misstep that your wife's worried about?
Offending guests with unnecessarily sturdy edges? Appearing as though a "real" dining table is an unaffordable luxury beyond your reach?
Ask her to elaborate until she can articulate her true reason for thinking it inappropriate. Then, laugh at her.

What does she actually want?
No one's answered your questions yet, and I can't answer them either (except that I'll recommend calling Herman Miller; they're pretty helpful on the phone), but "wrong" or not, your wife's feelings about your Eames table ARE her feelings. There's no upside in ignoring them, so I can't say that I concur with the advice you've gotten here so far.
Therefore... Even if you can remove the rubber edge and successfully replace it with veneer, I don't see the point unless your wife has always dreamt of having a veneer-edged Eames conference table in her dining room. If her ideal dining table is something else, maybe it'd be better to buy one of those and keep using the Eames table as your desk.
Just my opinion, of course.

My answer
To your questions... I'm gonna say yes, and no.

yes and no indeed
I've worked on hundreds of metres, probably a few kilometres worth of this stuff so to answer the question, no its not simply a matter of swapping the edge, for a few reasons. They are applied with a hot melt adhesive with special machines, you can iron the strip on if you have some dexterity and if its birch or something plain you could probably find a match if you look around, however you'd have to buy a roll. You won't get a full bond on the surface because of the slot. You would then have to join the strip and remove the excess which can be done quickly with an old plane blade if its thin or with a round over bit in a small router if its thick. You'd then have to finish the edge.
I forgot, unless you use a primer to help the glue bond it can come off very very easily, especially on particle board.
Does the table have curves? The only thing that I think would be ok would be to remove the strip, take the top to an office furniture manufacturer and if they can match the veneer ask them to apply a thick edge.
Call Herman Miller, I doubt they could help you and would just suggest a new top.

I like that rubber edge
on my Eames dining table; it matches exactly the side and back of my 4 EC127 Eames chairs.