OK, but just remember you don't want to switch the generator neutral. The only neutral reference for the generator is the power neutral. It may not cause any problems but it would leave the some circuitry in the generator unpowered and the references having no return. Obviously in an emergency this would not be an issue but throwing it off at some other time might be. Also 60A is not rated for anything over 14KW. The purpose of the box is for two things, most importantly a disconnect and also a cable transition point.
I hear the term "fused" used and not being an electrician I don't know if this means that fuses are actually used verses a circuit breaker or if the term simply means protected. I suppose it does not matter but cartridge fuses tend to fail with age and you never have a replacement around when you need it. I would opt for the breaker. You don't need circuit protection here so a non protected disconnect would work just as well but the more mass produced ones, like the two I pointed out with a 100A DP breaker are a lot more reasonable.
I do not plan on switching the neutral. I will split bolt them together. Since the unit has its own breaker I do not need an additional one. My 5870 is only 8kw so 35a is max. A 60a non fused disconnect is proper. A fused disconnect allows you to install a 60a disconnectfor example and fuse the load to what is the max amps allowed per nameplate rating.