Who says you have to have an exchange with alcohol?
(And I know - everyone is rolling their eyes ...
Why not try doing a basic fun event - and just have no alcohol, which then you can have at EITHER a men's or women's house
Ideas like
Indoor croquet (use nerf balls please)
Murder Mystery (everyone gets roles, dress to character)
Snow soccer
A dinner exchange
etc. etc.
This would cut down on costs - from the chapter, the members, etc., and can be just as much fun as doing at a bar ... just keep an open mind ...
Just a thought ....