Wait you wouldn't take your cat? After a week of you rarely being available you consider not being home at all for two days and a night?

I would strongly recommend against that. I'm worried that this may cause behavioral issues with the cat getting bored, depressed, feeling caged...

Possible consequences could be urinating outside the litterbox, willfully scratching your furniture/walls and more.

I'm not sure if with your work and travel habits a pet would be a good choice. Maybe one that doesn't need social interaction?