Ew ew ew ew ew. I have done much slug research recently after the stupid little things viciously murdered my rhubarb plants. So hopefully I can help!
You can get "organic" slug pellets which are supposed to be pet safe. They're used by people who want to poison slugs but keep hedgehogs, birds, etc. from dying in a similar fashion. Now I did a lot of research on this, because I wanted to use them in an allotment which would be harvested mainly for my pigs' consumption. There is a lot of debate over whether or not they are in fact pet-safe, but the consensus seems to be that unless an animal actually ingests a reasonable quantity of the pellets themselves, they won't come to any harm.
The copper thing, I have often read doesn't work very well unless it's pure copper (an old wives' tale is that you can use pennies, for example, but most of the interwebs has told me this is rubbish and people watch them slide right over with no problem), so... You can try it, but apparently it needs to be a reasonably thick barrier and pure copper. Which isn't all that cheap.
In fact, this is the case with all barrier methods. Coffee grounds and/or eggshells are often recommended, too, but it needs to be a reasonably thick barrier and I don't know anyone who uses enough coffee or eggs to keep such a thing topped up all the way round a hutch.
Another option is to get some kind of rough... something. Mulch, gravel, pine needles, etc. and set your hutch on that. They don't like to crawl over it because it can gut them. Slits their soft underbellies right open, and I have no sympathy whatsoever! I think pine needles are especially effective because in addition to being sharp, slugs are repelled by the smell anyway. So if there's a pine tree in your garden or nearby, have at it!
Beer traps work well; as mentioned, margarine containers or empty yoghurt pots are great. Bury them in the ground with 1-2cm sticking up and fill them with cheap beer or even cider. (I buy that strong, cheap, and disgusting Frosty Jacks stuff. It comes in a plastic bottle so you can re-seal easily.) You can buy proper slug traps for this purpose as well; they have a little lid to keep rain and such from diluting your yeasty fermenting drowning pools. (I got 6 off ebay for a few quid.) Slugs can detect food up to a metre away, I think it is, so traps like that on the ground should attract them well before they get wind of you guinea pig food. They fall in and die happy. But I won't lie -- emptying them is a disgusting task. Especially if you forget or put it off for a few days while there are slugs in there and well... I don't want to talk about it. <(>.<)>
If all else fails... buy a pet goose.
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>>> poor piggies. I think you can get copper metal strips to put round plant pots to stop slugs, apparently they wont crawl over the copper ? so maybe you could put that on the piggies houses
