DL has not had a true night time parade (like Spectromagic) for many years. This is partly because it already has two major night time draws in Fantasmic and the fireworks. At Christmas it has the Fantasy parade which is a night time parade. In June there will be an evening parade that shows usually at 6:30PM so it is still light out. DCA has had the EP which showed at 8:45PM but as you noted it is going away.
The specific answer to your question depends on when you go in June. The first half is considered off-season and that means week days will have minimal entertainment. The last half is high season and entertainment is daily.
The best gauge for this June is past Junes. See "Historical DLR Park Hours, Entertainment and Refurbs" -
www.disboards.com/showthread.php?t=2291124
As for weekday entertainment see "What You Should Know About Off-Season at DLR"
www.disboards.com/showthread.php?p=18462889
Be aware of grad nights - "The Scoop on Grad Nights at DLR in May and June" -
www.disboards.com/showthread.php?t=2298400
And be mindful of AP Blockouts which will have a huge, huge impact this June - "Understanding AP Blockouts and Impact on Crowds"
http://www.disboards.com/showthread.php?t=2365983