How many hairs per sq. cm. (or inch) do hamsters have on average?
According to Paul et al. (2007), shaved fur patches of male Siberian and Syrian hamsters had a mass of about 12 mg/cm2 dorsally and 3 mg/cm2  ventrally.
This search give me the page.

Fig 1 from Paul et al. (2007) compares mass of fur growth across time for 2 groups exposed to differing lengths of daylight (long, LD, and short, SD) to examine winter fur adaptation.

Paul, M.J., George, N.T., Zucker, I. and Butler, M.P., 2007. Photoperiodic and hormonal influences on fur density and regrowth in two hamster species. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 293(6), pp.R2363-R2369.