Hi,
We have worked a lot on the creation of e-commerce website working with Majento (among many other CMS). We have a good experience for the maintenance of such website and so with update process.
We are able to perform the update you need, fastly and without the need of putting your website offline, we have our own production/test server.
We will then export all your files and database to our production/server, to perform the update away from your own server, and then once everything is ok and verified, we will then replace every files and database on your server. this way your service will not be interrupted.
Waiting your reply
Thank you