Here is the text in Swedish: SFS 1988:254
1 § Knivar, andra stick- och skärvapen och andra föremål som är ägnade att användas som vapen vid brott mot liv eller hälsa får inte innehas på allmän plats, inom skolområde där grundskole- eller gymnasieundervisning bedrivs, eller i fordon på allmän plats.
Förbudet i första stycket gäller inte, om föremålet enligt särskilda föreskrifter ingår i utrustning för viss tjänst eller visst uppdrag eller om innehavet annars med hänsyn till föremålets art, innehavarens behov och övriga omständigheter är att anse som befogat.
If I understand it right it says that you are not allowed to carry knives or other items meant to be used as weapons in public places or schools. I guess it is a question of INTENT. A knife to open boxes, cut strings and other good things is ok even at a school. The same knife brought for the purpose of self defence is NO NO.
The second part of the text states just that.
However a knife meant for good can be used for evil if the circumstances are wrong, thats is why you should not bring it to the bar/pub etc. (A court ruling allows SAKs and similar).
It depends on when you arrive, but June 6 is the swedish national day and hence a holiday.
Here is some sketchy info on outdoor activities
http://www.koping.se/kopingtemplates/Page.aspx?id=1377
One easy way to avoid fuss with the customs, you know terrorists, Dunkin Donuts and all that, is to walk into any sports store or hardware store (Bauhaus, OBS, Clas Ohlson, JULA etc) and buy yourself a Mora 2000 or any Mora clone. That will be enough for your needs during your stay and not too hard to loose in the customs.
One other way is to email someone at the company you are visiting and ask them about ideas what to do. There are usually at least one outdoor cracy guy at every place. Because of the "Allemansrätten", the right of public access
http://www.naturvardsverket.se/en/In-English/Menu/Enjoying-nature/The-right-of-public-access/
you are allowed to walk almost anywhere in the outdoors.
Good luck on your trip.