Hello and thank you for using Just Answer,To hav ethe stock signed over to her directly would protect you from taxation on the sale. The transfer of the property to her would fall under the settlement of property if you sale the stock and then give her the money you would not report the money you transferred to her but your sale of the stock would be a taxable event for you. If a gain then you would pay tax.This account is not like a retirement account that must be divided so you would not be allowed to use the Qualified Domestic Relations Order.
QDROs may grant ownership in the participant's (employee's) pension plan to an alternate payee (the ex spouse) so the payments are made directly to the ex and not through the spouse that originally held the retirement account.
Generally, there is no recognized gain or loss on the transfer of property between spouses, or between former spouses if the transfer is because of a divorce.
If you were transferring the stock and mutual funds to her this would not be a taxable event for you then if she sold she would have the taxable event.
I would suggest you get your attorney to see if you can transfer the stock in lieu of the sale and not jeopardize your settlement arrangement.
Wanted to touch base with you and make sure all worked out. I never heard anything from you after my post but would be interested in the outcome of your posted question.