There is a known issue for some users with changes made to the Software Updating part of Health Check.
A fix has been promised hopefully sometime this week.
In the meantime there are a couple of things you could try:
1- Using the seperate Tools>Software Updater in CCleaner to see if that one will update the problematic apps for you.
2- Looking at what software Health Check has found to update and then update them manually yourself.
If/when they have been updated then Health Check will no longer hang trying to update them.