you can run cables between floors, and it won't make a massive hole. Buy cable the length you need (or get bulk cable though you probably won't need it) and cut off the connector on one end. Drill a hole just big enough in a corner somewhere or wherever is appropriate (will depend both on where the cable is going and how you house is built).
Once the cable is passed through attach a new RJ45 connector to it, for this you'll need a special tool to squeeze the connector in place on the cable, and you'll need to follow a pattern for which wires go where.
You can probably get the tool at the same place where you can find a long enough cable. and RJ45 connectors too.
A lot of people don't do this because they have to buy the tool and they're like "I don't want to buy this just for one cable" but you keep that tool for life and it can come in handy for future projects, especially when moving out.
Tool:
http://www.newegg.ca/Product/Product.aspx?Item=N82E16899888401CVF or local shops in montreal:
http://www.microbytes.com/product_info.php?manufacturers_id=&products_id=30085&osCsid=50f43ecf424d7b96861c4c786912b155
You can probably get everything at the same store though.