Well, they don't need to dance really or sing all that well. They only need to make funny sing-song lines that fits their character. You don't need to stay completely faithful to the song.
This WoW parody for example manages to perfectly use their own original lines. You could do something similar.
I can help you along with character suggestions. Here's a faithful version that completely copies the original video:
Kanako: It never gets old. huh?
Suwako: Nope.
Kanako: It kinda wants to make you want to...
Suwako: Break into song?
Kanako: Yep.
Suwako:
I love the mountains~Kanako:
I love the clear blue sky~Parsee:
I love big bridges~Cirno:
I love when great whites fly~ *Letty is flying in the background, clearly annoyed at/insulted by Cirno*
Hatate:
I love the whole world~ *is hiding in bushes with camera, spying at the SDM in bathing suits at the Misty Lake*
SDM:
And all it's sites and sounds~Chorus:
Boom de ya da~ x3 *three panels of SDM trying to capture Hatate for peeping on them*
Flandre:
BOOM DE YA DA!! *Flan comes blasting out of the basement and walls, proceeding to cause havoc among the SDM and Hatate*
Murasa:
I love the oceans~ *Murasa is standing epically on the bow of her ship (Gurren shades optional)*
Yukari:
I love real dirty things~ *Yukari is reading 'questionable' magazines while having a nosebleed*
Youmu:
I love to go fast~Keine:
I love Egyptian kings~ *Keine's teaching her class about Egypt while using a wrapped up Mokou as a living example of mummies. Mokou's obviously unamused.*
Byakuren, Shou, Ichirin and Nazrin:
I love the whole world~ *stand in front of their shrine praying*
Reimu:
And all it's craziness~ *Reimu watches the usual What-The-F***ery around her Shrine while sweatdropping*
Prismrivers:
Boom de ya da~ x3 *huge concert with most of the cast*
Utsuho:
BOOM de ya da!!! *nukes Gensokyo*
Aya:
I love tornadoes~Kisume:
I love arachnids~ *Kisume hugs Yamame. Cue d'awwwwwws <3*
Yuugi:
I love hot magma~ *chilling in a magma pit along with Suika, acting like it's a hot spring*
Sanae:
I love the giant squids~ *hearts in her eyes while staring at Nue* Nue: Stay the hell away from me.
Marisa & Alice:
I love the whole world~Bulk of the cast:
It's such a brilliant place~Background:
Boom de ya da~ x2 *Mokou sets Kaguya on fire*
Evil Eye Sigma:
BOOM DE YA DA *close up on its creepy eye*
Rinnosuke:
Boom de ya daaaaaaaaaaa~ *falls down pit*
Like that, Muffin. Of course, it would be most fun if all the characters got original lines like the WoW version and not be directly copied. I just posted this here as an example of how lulzy it could be. I won't blame you if you don't feel like doing it, but I'm just saying it could have lots of potential.