Same problem here... We upgraded most of our websites to DNN 962 and even 971 but It was quite a struggle with the modules (dnnharp, easydnn, dnngo, mandeeps, core modules etc.) that are not compatible with the latest DNN Version because of the removed deprecated api methods.
We decided never to perform an upgrade in production but make a local test copy and test the upgrade. Make a script/log with the modules that need an upgrade and make sure you do it in the right order.
We succeeded in all upgrades and had to rebuild (find an alternative module for) some modules that aren't supported anymore (dnn360 cissmenu, form master 2008, ventrian newsarticles, DNNSmart etc.)
Oke it took some time, but we get rid if the old modules and have secure, stable and high performance websites now.
There still is an issue with DNNSharp modules and the upgrade to DNN 9.7.1.
But DNNSharp will release a fix soon!