Moving DBs (including System DBs) to new LUNs on a single node cluster
As long as the path names remain the same for your database files, this approach should work.  This assumes that when you say "copying all files", your are ONLY moving the database files (data/log) and not the SQL Server binaries.  If your SQL binaries and/or resourcedb need to be moved, you have a much stickier task ahead of you.

Your biggest gotcha should be maintaining the directory and database file permissions.  I would handle this using ROBOCOPY with the /copyall switch to move the files while keeping all perms and attributes intact.

While outside of scope, if your end goal is to move the database to your full cluster and you're hurdle is client connectivity, have you considered using a DNS Alias to redirect traffic?  I understand that the connectivity change could be larger in scope, but it could give you a path to consolidating your databases to where you want them.