Can I slope a patio left to right

[questionmark]

I have a summer house located at the far end of my garden, connected to the main house by a decking walkway. Eitherside this walkway are large green spaces. Due to the decking deteriorating after 10 years, I'm planning to replace it with garden slabs. However, I'm aware that the slabs need to be sloped for water runoff. The walkway is about 10m long by 1m wide.

My concern is that directing the runoff towards either house would be problematic.
Another question I have is if I can slope it horizontally, will the slope be noticeable to people walking across?

I have provided a diagram and the yellow arrow is what I am talking about when I mean horizontally

 

[foxhole]

No problem , though a level path isn’t going to flood.

 

[questionmark]

Do you think I can get away with no cementing the slabs down. I just want to do a sub base and a layer of sand to seat the slabs in...

I have slabs vertically placed along the length on both side as a "retaining wall". Dug down about half away in the ground. The slabs will seat in between them so im not too worry about it moving left or right...