<<I am 35 years old and have recently resigned from my present company.
With repect to my 401(k) program, I understand I have the option of
leaving my money in the existing program or can transfer the balance
into another similar type of program once I begin my new job. If
possible, rather than placing the balance into another 401(k) program
(which consist of mutual funds with varying degrees of risk), I would
like to redirect the monies into individual stocks. I also realize the
money must remain under a "retirement vehicle umbrella" to be exempt
from taxation. Is there such a program/vehicle?>

Mai oui!, as the French say.

Just roll it over to a self-directed IRA. We've done this twice with my wife's 401(k)'s when she left her last two jobs. Ameritrade, or other brokers, will give you the forms to do this.
Ray