Can I play "Archie's Ace in the Hole" or "Maxie's Hidden Ball Trick" if I don't have a Water/Fighting Pokemon in my discard pile?
No, you cannot. If you can't put one of those Pokemon onto your bench you don't get to draw 5 cards.
Source: TPCi Rules Team (2015-02-26)

Relevant cards

Note: All applicable cards may not be listed below.
XY5_124
XY5_133
XY5_157
XY5_158