The biggest issue is that on MTB shoes, the rubber sole will wear away even slightly, and you will be walking on the cleat, which is not a good thing for a hike.

The best combination shoes for cycling and walking are proper hiking shoes. Low ankle ones, with a decent thickness sole that is stiffer than running shoes. The thicker, stiffer sole will be important if you are pedalling 120km a day.

If you are going to go without MTB shoes, I would ditch the double-sided pedals for the trip, and just fit platforms, maybe with clips and straps. MKS makes some nice ones, I think, and they are Japanese.

If you do decide on clips and straps, and with something like hiking shoes, you may need to fit a spacer to get the spindle of the pedal under the ball of your foot, rather than towards your toes.