Can I use Jynx's "Mimic" attack to shuffle my hand into my deck when my opponent has no cards in his or her hand?
Yes, but you won't draw any cards after you shuffle it in.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)

Relevant cards

Note: All applicable cards may not be listed below.
DP5_55
HGSS1_69