What are the high level steps for the above?  Something like this?

1. Move K2 server from on-premises to Amazon AWS - it will remain accessible to the on-premises SP2010, so nothing should break.

2. Upgrade K2 to 4.6.7 or better - again, nothing should break

3. Configure K2 IIS sites for designer, workspace, etc. to use HTTPS, and update environment tables to match - might hit client browser security issues here, due to SP2010 sites being HTTP only

4. Migrate site from 2010 to SP Online, using 3rd party tools.

5. Deploy K2 for SharePoint app to migrated site

What are the steps at this point to migrate the K2 elements for a SharePoint site?  Copy process and then deploy copy to the new (migrated) site??

(I'm not a K2 guy, or a developer - I'm a SharePoint infrastructure guy)