Squash is the gone of the worst edge killer.
If you own a more expensive Japanese knife, you should be wary to use it to cut squash.
Yes, with proper technique you could do it safely, but people get tired, the knife can slip and you can ruin your expensive knife.
I would use a cheaper knife with the typical German or equivalent stainless steel. Alternatively, and carbon steel (now 1075) Old Hickory Chef knife or a larger butchers knife should take the beating.
A cheaper bread knife is good to cut the squash into more manageable pieces before you cube them further.
If your recipe allows it, microwaving the squash briefly softens the skin significantly.
You don't have to use the same knife for everything and you don't have to risk ruining a nice, expensive cooking instrument like a Japanese knife trying to prove it's capable of cutting a squash.
Just my $0.02, YMMV.