In a rare case of disunity between two champions whose pairing has been notably harmonious, Hamilton said forecast rain on Friday would be a setback for the team in what has been billed as a key test of new aerodynamic components.
Button, the reigning Formula One titleholder, feels it would make no difference.
"You can't really test things in the wet, that's why at a wet test in Jerez you don't really do anything," Hamilton, his jacket still damp from the rain lashing down outside, told reporters.
"It's difficult to get good readings because the grip is so low. So we have to wait and see," added the championship leader.
"If it stays wet all weekend, we might have to do our testing at the next race."
McLaren tried to introduce a new 'blown diffuser', a system channelling the hot exhaust gases down and out through the rear of the car to create more grip, at the previous British Grand Prix but had to ditch it when it proved problematic in Friday practice.
The team, top of the standings despite Red Bull having taken nine out of 10 pole positions, intend to try out a modified version this Friday before deciding whether to use it in Sunday's race.
"I think we're confident we've made another step forward in understanding it and trying to improve it and make it work better than it was then," said Hamilton.
"But we still plan on running loads of sensors to understand it fully because I'm sure it's still not optimised."
Button has no doubts it would work.
"It will still work in the right way in the wet, so you will still get the right information back. It's not a problem," he said.
"Our heat issues we have pretty much sorted. It's just finding the performance in the floor (of the car) that we didn't completely find in Silverstone," he added.
"I don't think this really hurts us too much, we can still get some really good running done on Friday and useful testing.
"The bigger problem this weekend will be the tyres," said the 30-year-old.
Bridgestone have brought two tyre compounds to Hockenheim that are widely divergent, one super-soft and the other hard.
Drivers have to use both in the race and the challenge will be to figure out how long the super-soft will last before deteriorating and whether to start the race on it or go with the harder but slower tyre.
Wet conditions will make that even harder to assess.
"It will be nice to get some running on the tyres before qualifying," said Button. "I've heard that the super-soft is very soft for here and the super-hard is very hard for here.
"So it will be interesting to know which one we run in qualifying. The super-soft is a quicker tyre if you can get it to last for a lap.
"I think we will see some interesting strategies like we saw in Canada [ Images ], people trying different things," Button added.
"If the super-soft is going to grain as much as we think it is, how many laps are you going to do (with it) in the race? It might end up being a two-stop race for us."