Scott, you have a 'flag' mirror ... not an electronic mirror. the post of a BMW ad has an electric mirror on it. the passenger flag mirror is available thru W+N for around 118 euro +/- plus shipping.
no, i wouldn't think of put the fender mirror on and leave the flag mirror on ... kind of like belts and suspenders ... except in this case you will be looking at the flag mirror in the fender mirror. i'm not going to say that there hasn't been a coupe with the talbot mirrors on (other than a 2000 cs) ... but it would be a rare.
i drove my brother's austin healey 3000 a lot and it had the fender mirrors (with convex mirrors) and i liked that you could glance down and see to the side ... but the shape made everything so small that i really hated it. before you invested in them, i would find some british car with them and sit in it and see what you think. IMHO, if you want to improve the visibility out of the flag mirror, i would explore moving it forward to where you look thru the vent window to see it ... the euro position at the front of the door.