I know that my skin turned orange at a time when I was consuming
large amounts of them -- they were the principal item in
my diet at that time. (I consumed loads of citrus for over
6 months before the orange tint was visible.) I was consuming
carrots as well at that time, but in extremely small quantities.

If you are so worried about this, just remember to look at your skin
(untanned sections) in a mirror. The orange tint starts out very
faint, but eventually will become noticeable, assuming your
vision is unimpaired.

PS are you assuming that the only source of the orange color is
carotenes? Given that plant foods are rich in colors provided
by flavonoids, you might want to look into that as a possibility.
Other chemicals (besides carotenes) might be contributing to the color.

Tom Billings