Upgrading from Kentico 9 to 10 is a little more of a step than from 8 to 9. I don't see anything in documentation concerning this, so i can't say for positive, however having done many upgrades, i cannot recommend you do a major version upgrade on a 'live' site while it is still live. Hotfixes are fine as they are very low risk and don't take a lot of time, however for major upgrades i would highly recommend you initiate a content freeze, pull the site down to a local environment, upgrade, then push the upgraded solution, replacing the old version.
Another option though if you still wish to do it live but have a better offline page, is to not rely on Kentico's offline mode settings and add a custom offline page (say _offline.html) to the root of your site, and then in IIS on your site go to the configuration editor and set the default page to _offline.html.