Bloodrunsclear: Just wanted to tell people who, like me, might run into this problem that the game does not elaborate about.
In Deadside you will come across ropes you can grab but you cannot seem to climb across.

Hit Tab to open the inventory
Click the Spirit Gun (it looks like a skeleton gun and it's set in one hand slot of the inventory)
You will put it away, free both your hands, and now you can climb onto any rope and climb across it!

Also after you jump down just click again twice. In the remaster thankfully Shadowman will reequip his gun without asking so you won't take unfair hits just because you finished climbing across a rope.

TaxAkla: Just found that to put off the guns click on the Action Key, the letter E.