Yes, using an access point is very straightforward. You'll connect the device to the original Sky Router via a Cat5e cable and, set up as an access point, the device will create a secondary wifi network in the house. This secondary wifi network should preferably be named differently from the first one - for example "Family Network 1" and "Family Network 2". Network 1 would be the network of choice downstairs and 2 would be the network of choice upstairs. All that needs doing is to set up the new network on all the mobile wifi devices in the house (laptops, phones...etc...). If there are any wifi dead zones in the house, the devices will switch automatically to the other network when they lose one of the signals. If there are no dead zones (only areas of very weak signal), the users will have to switch manually (which literally takes one click). But very likely, if you position the new access point strategically upstairs, its signal will probably flood the whole house, making the original wifi signal from the Sky router redundant. That's what happened in my house, which is larger than the average house. The Sky router only offers a very sub-standard signal, strength-wise.
Using the device as a repeater is a possibility as well - in this case you won't need to use any wired connection between the Sky router and the device. The device will pick up the (weak) signal and will repeat it, full strength. In this case, there is only one wifi signal in the house, so there is no need to set up anything on the laptops and other devices. The drawback of this method is that you lose half the wifi bandwith from the repeater (it gets a bit technical here, but just trust me on this). Also, if the signal coming from the Sky router is inconsistent and unstable where the repeater is set up, then you'll end up with a very unsatisfactory solution overall.
That's why I would suggest going down the access point route. It will not affect the Sky Conditions of Use or anything, since you will still be using their router to connect to their network. The access point will behave like a normal peripheral hooked up to the router, no different from a computer or anything else. Sky have absolutely no way to know that it is being used, and even if they did, it wouldn't bother them at all - it is just an access point, not a modem!
Besides, contrary to general belief, Sky care very little whether you use their router or not. They won't provide ANY support whatsoever if you are not using their modem to connect to their network - but if someone is using their own modem and it is set up properly, they won't pull the plug! What has been happening in the last few years is that Sky has been changing the access protocols to their internet network, slowly moving whole areas from standard PPPoA over to a modified version of MER. Those people in those areas using their own modem lost their connections - not because Sky pulled the plug, but simply because their modem could not handle a MER connection. There are very few compatible third party modems. But with a compatible modem, and provided the user knows their Sky internet access username, it is possible to connect - and Sky won't pull the plug.
Some areas, like mine, currently have the dual connection (both PPPoA and MER), which means that it is still possible to use any third party modem, or the Sky router. But when they remove the PPPoA connection, anyone not using the Sky router or a MER compatible modem will lose their internet.
I am not saying that Sky never disconnected anyone, but there is no reason to get paranoid over that issue. They just don't want Joe-Customer messing around with the internet settings and messing everything up. But for Mr Geek, there is no issue. They just won't help if things go wrong. But then you can always re-connect the Sky router...
To get back to your issue, note that -depending which Sky router they have- it might provide an N wifi signal (as well as G). The Netgear device you provided a link to, is G only. It is not a problem as such - it will still work well, but if the family use N devices (mobile phones, XBox, laptops...etc...) those won't get an N signal from the secondary network, only a G signal. It's not a problem, it'll still work, and likely they won't see ANY difference whatsoever, but it's worth noting.
Hope all this helps. Hope I didn't confuse you more than necessary! Have fun!