The new non-security patches are described as "cumulative." I take that to mean that installing one of the new non-security patches (such as KB 4016240) will automatically install everything in the previous cumulative update, which may include security patches.
Will it be possible to install these new non-security updates without installing the preceding Patch Tuesday security update?
Every update we release is cumulative. So a new non-security update contains all the previous security and non-security updates; a new security update contains all the previous security and non-security updates.
So if your goal is to avoid a particular fix, that would mean never installing another update - every update we release will contain that fix.