|It's strictly wired - unless you include a plugin wifi module. Netgear make one (as do Devolo). And I think most of the other manufacturers do as well.|
The "only possible" problem you "may" have is if the there is an RCD in the cct. - in one or both "boxes". Some pholks (at least in Canada/USA) find that gets in the way and prevents the adapters working across some power ccts. Personally, although I have an RCD (sorry GFI - Ground Fault Interrupter in Canada/USA) in one of my two consumer units/"boxes" and not in the other - I have no problems at all with powerline adapters communicating between the two boxes and their respective power ccts.
To clarify my setup a little? I have two "breaker boxes" - aka consumer units (in the UK) - in my house. Logically they are fed/controlled by the same incoming main electrical feed and metered etc. by the same meter. There are power ccts. in both boxes. - those in the non RCD/GFI box are reserved for fridge freezer etc.; and what used to be an office area - with assorted IT kit. I still have networked kit in there. The other "box" - with its RCD/GFI - is the bulk of power distributed around the house... The Devolo kit talks/connects fine between all power ccts. in both consumer units/"boxes".
There have been discussion here between pholks in Canada/USA who have on occasion had problems with an RCD/GFI being in cct. (in the respective breaker box(es); but many have found it to be no problem...
I would suggest you investigate the powerline approach first. Test it and if it doesn't work (try it with cat-5 at both ends first) then return them? Amazon allow returns (30days period as I recall); and likely many decent computer etc. stores (online or on the street) will allow returns if they don't work for you?
The powerline approach, with a wifi adapter included in the shed, is the simplest to set up. And with the wifi module/adapter included you would have the required wifi for phone etc. Equally if the powerlines do work then you also have the option to add in a second router, and configure it as both wifi extender and of course gain four more cat-5 ports in the shed?
If powerline adapter path doesn't work for you, then you are into actual cabling and a wifi extender or a second router in the shed, configured as a repeater etc...