Answered[ Edited ]
La vanilla have lots of simple fragrance, vanilla, or vanilla+grapefruit or vanilla+lavender etc, and they are not super strong or musky. Something like this perhaps: http://www.sephora.com/vanilla-summer-P311183?skuI
If you'd like to look at light fragrance, DKNY Be Delicious (the one in green) is very light even right out of the bottle. It's fresh, slightly fruity but not sweet, and mild (not powdery or crisp/sharp).
I would second the idea of looking to the series of LaVanilla fragrances.
Other than that, you might want to consider Acqua Di Parma's Blu Mediterraneo Mandorlo Di Sicillia. It is just lovely, although a bit expensive. It is definitely vanilia, but mixed with something of cola and almond scent and then the dry down smells of just pure vanilla. I too, am not quite a fan of musky or floral scents, but love vanilla and ADP Mandorlo was perfect.
The link to it can be found here:
I agree with what has already been said. LaVanila has a number of different vanilla based scents. Pink Sugar is another sweet vanilla-like scent with caramel notes, it's really warm and light. I have a very sensitive nose too, and this fragrance never irks my sinus system .
I also wanted to add to the great recommendations that you have already. Have you tried the Pacifica Island Vanilla™ Perfume? It contains essential oils and have a wonder soft vanilla fragrance.