K2 Blackpearl 4.5 and Sharepoint 2013

I suspect the upgrade of blackpearl to the latest version will go pretty well.

I suspect your K2 API calls will also allm or almost all, work.

What do you use as your form enviornment?  Is it custom ASP.net since you mentioned a lot of custom code against the K2 APIs?  If so those forms should probably be fine.

Do you use a lot of K2 for SharePoint events in your process?  If you are planning on using SharePoint 2013 in native mode with the K2 app (instead of running the SharePoint site in 2010 mode) it uses all different K2 for SharePoint event wizards that go against the client side object model.  So those old SharePoint events would need to be redone in your process.

Here is an article that talks about moving K2 from SharePoint 2010 to 2013 that should help.

http://help.k2.com/KB001380

Of course lots of testing will be required regardless.

Okay so without K2 for SharePoint 2007 events you wouldn't need to remove those and use the new SharePoint 2013 templates (not that that is really that big of a deal normally).  I believe the process should most likely upgrade fairly smooth to 4.6.7 or might require minor changes. 

You mention asp.net pages and controls running on SharePoint 2007.  Although I would think the integration with the K2 API should work fine after the upgrade I suspect you'll need to make changes so that whatever controls you're running or integration with SharePoint 2007 works well with SharePoint 2013.  As well SharePoint 2013 like 2010 only runs in a 64 bit enviornment which could also potentially cause issues with your pages, controls and custom code.

If I were you I would try a quick migration in a controlled virtual machine environment and try moving across the process and some of the custom pages and controls to get a better idea of exactly the issues you'll face before coming up with some type of work estimate.  I hope this helps.