As far as I am aware, the transition advisor will show you what features you have now are supported with the cluster data ontap and it will tell you what isn't compatible.
I am in a similar position as you as we are on 7-mode and at some point would like to move to cDOT however you need to bear in mind that the filers need to be completely formatted with the new OS when moving to it you can not do a non disruptive upgrade from 7-mode to cDOT. There will need to be downtime and if you have data presented you would need to move the data to another storage device before you continue.
So why is it you need 8.3, are there particular features/improvement that would benefit you? As others have said, this isn't just an upgrade but a complete re-install from scratch. Keep in mind, depending on your hardware configs you may need additional network ports as well. If you don't need anything in 8.3 Cmode then I'd suggest leaving it as is. I still have a lot of machines running 8.1, and even a few on 8.0.
We recently did some professional services with our prefered NetApp partner here in the UK and when we looked at the feasibility to moving to cDOT they said we would need temporary storage to move our current data whilst the NetApp is rebuilt.
We have a similar problem as our NetApp is our only primary storage device.
They did mention that NetApp/NetApp reseller do have the ability to acquire 'Swing kit' where NetApp will temporary hire storage out to a customer for them to achieve cDOT migration if they have no other storage available however this will come at an additonal cost but the costs are reasonable as NetApp are keen for customers to move to cDOT and want to make the transition as simple as possible.
My recommendation would be to speak to your NetApp partner or account manager.