(Yes, there were fancy dress balls in the Regency era, though it's difficult to find much information on them. Note the distinction made here between the masquerade or characteristic ball, at which masks were worn and behavior was less restrained, and the more respectable fancy dress ball, at which masks were eschewed. This excerpt is from a lengthy satirical poem by London dancing master Thomas Wilson, who was active from approximately 1800 to 1825. The "some people" said to confuse the two types of balls are rival dancing masters.)
Fancy dress balls must as the next appear,-- Thomas Wilson, The Danciad. London, 1824.
And what they really are you now shall hear.
Fancy Dress Balls, some people likewise name
Characteristic, and think they are the same;
(But Characteristic as I just have said,
Is meant to signify a Masquerade,)
A Fancy Dress Balls that, where every guest
Is in appropriate costume strictly dres't;
The face to shew the character, and age
They paint, as is the custom of the stage;
The mask's forbid the countenance to aid,
For "Fancy Ball" means not a "Masquerade."