If your intent is to sell the stock, transferring it out doesn't make any sense unless you have a private brokerage account with free trades available. In that case, you could transfer the shares in-kind (no fee as per your plan), and then sell them with no fee via your brokerage. This isn't the norm for brokerage accounts, but some offer X number of free trades if you have a certain balance or account level.
If not, just sell them where they sit and transfer the cash out to your brokerage account, wherever that may be. May take a couple of steps to do this...ACH to your checking account, then up to Vanguard (or whoever).
My employer's stock plan is administered through Merrill Lynch, which doesn't fucking offer ACH transfers from this type of account. Which is total bullshit. They offer wire transfers (at a cost of $7.50). I opted for a check. Vanguard offers mobile check deposit, which is how I'll be getting the cash to them.