A good description of the WMAP scan geometry is on the WMAP website. A good description of the COBE scan geometry is in Smoot et al, Astrophysical Journal 360:685+, p. 686.
From the COBE description, it seems that to first order in Earth's orbital eccentricity, a nearby non-Lambertian emission shell for the CMB would not affect the apparent dipole. However, the article admits that there was enough deviation from the idealized description, that sometimes part of Earth appeared over the edge of the sunshield. So, an effect on the apparent dipole might be seen due to the COBE scan geometry. It likely would be smaller, but of the same sign as, that due to the WMAP geometry.
WMAP, basically, scanned the hemisphere away from the sun. A non-Lambertian emission surface at 52.6 AU (e.g., a sum of rainbows) would give an apparent cross dipole of strength
0.5/52.6^2*(90/theta)^2*8/pi*epsilon
where epsilon is Earth's orbital eccentricity and theta is the angular radius of the "rainbow" (the rainbow is a model of extreme non-Lambertian emission).
By the method of Newton's "Optics", Book I, Part 2, Prop. 9, Problem 4 (pp. 446-447, Britannica Great Books edition) one sees that the index of refraction which gives the largest deflection (39.4deg) for light transmitted through a droplet, is sqrt(2). The light reflected in this droplet gives a rainbow radius of theta = 31.6deg.
Using this as a model or guide, one finds that Earth's orbital eccentricity causes WMAP's apparent CMB dipole to lag 3.0 degrees. The actual lag found above is 3.1 degrees. COBE's smaller lag (0.6 deg) might be due to a lesser amount of the same phenomenon.
