There should be an insert in the mouth of the scabbard and that holds the receptor for the catch which you can see on the sword. This would have locked the sword firmly in place.
Yes, you should keep the sword in its scabbard, but please remove the 'Rem(ington)' gun oil? Go down to the chemist (pharmacy) and buy yourself some Clove Oil. It is made from the stuff your mum used to put in apple pie

Wipe the gun oil off with a Kleenex. Admittedly, I am teaching you look after a pristine polished sword... but hey one day. Take the clove oil and put a drop of clove oil about every 6" down the blade. Wipe this carefully down the with your thumb with your index finger on the other side of the blade. This is the only time you will touch the blade with your fingers, and you will not allow anyone to touch the blade with their fingers on pain of loosing them and you will tell this to anyone that handles the sword before they are allowed to hold it. Turn over the blade and repeat. Now rub the blade with both finger and thumb until you can feel the the blade has a thin, even covering of clove oil. Now take a clean, Kleenex, and make one pass from hilt to tip. Replace the blade into the scabbard. There is a correct way of doing this, but it takes about 6 months of practice to get it perfect, so we'll leave that. There is a samurai film 'Shogun' with Richard Chamberlain if you want to learn it, or watch any film with Toshirô Mifune who is also in Shogun. You will recognise his face. Click here, and click on the Alltheweb 'Pictures' tab.
http://www.alltheweb.com/search?cat...q=Toshirô+Mifune&rys=0&itag=crv&_sb_lang=pref
This shows you the correct way to draw the sword.
Just noticed senoBDEC's post, and yes it is a good idea to have a 1" piece of blade polished. You pay for polishing by the inch anyway! This will show you if the blade is a good one. Once the blade has been profesisonally polished it will have a mirror finish and that is where the careful handling begins in earnest.
I just found this site which shows the insert on the scabbard and what it looks like under the hilt.
http://www.johnnyg.westhost.com/swords-japanese.html
We have 30 cm of snow coming here in sunny Toronto from tomorrow at noon!