One might think that there is already a similar question
on this matter. However, your exact question is a bit different.
An Upgrade Approach
As far as unwiring the existing DI containers (and updating Sitecore), I would start with trying to eliminate upgrade complications first.
1. Start with just removing your old DI completely.
While this may seem like a backwards approach, upgrading to Sitecore 8.2 with a DI container already in place, or customizations to the MVC Controller Initializer in the initialize pipeline, can complicate the upgrade. So, unwiring it to begin with can remove an upgrade variable.
2. Upgrading your environment to 8.2 (or fresh install depending on your approach)
Perform the upgrade to your needs. If coming from anything before Sitecore 7.2, consider a fresh install. If coming from 7.2 directly, consider the Migration Tool. Anything past 7.4, follow upgrade path documentstion.
3. Applying your controllers and modules following Kam's blog.
Now with Sitecore upgraded and the default MS DI in place, you can wire your controllers and modules back in using the configs.
There are a couple approaches, but you don't have to "upgrade to MS DI" in order to use it. Instead, Sitecore has created a series of configuration files that allow you to patch in your DI elements. As long as you don't need any real elegant work registering controls, you should be ok.
In my opinion Kam Figy wrote the leading blog post on how to work with the Sitecore MS DI. This should help you understand how to do the config.
The other question that is of a similar subject matter, linked above, has a really great answer on understanding what you can do with it.
One of those approaches is using your current DI in addition to the Sitecore DI.
A second approach is to unwire the MS DI from Sitecore and implement using your own.
Mileage may vary, and your exact solution is going to be heavily influenced by your current container needs and existing code base.
As with anything, this is an approach. There are others, and the right approach really depends on your solution and the intricacies of it.