Generally, ἐνδιδύσκω is used in the present and imperfect, ἐνδύω in the aorist and perfect. (Exceptions: two ocurrences of ἐνδύω in the present, in Mk. 15:17 v.l. and Jer. 1:32; one in the imperfect, in Ps. 34:13.)
See discussion:
http://lists.ibiblio.org/pipermail/b-greek/2000-December/014685.html
to put on under (v.) metaph., κίνδυνον ὑποδύνειν undergo danger; intr., slip in under; put one's feet under a shoe, put on; metaph., insinuate oneself into favour with