I'm wondering why your wife wouldn't have accounts in her name or why you two don't have joint accounts? For many reasons DW and I have Vanguard accounts in her, mine and joint names. If either gets sued, individually, you don't lose it all. But, I'm probably not answering your question; if all you would have with UBS is the stock, get it into something else, cutting your fees in the future. Depending on account size, you can sell, buy, trade much cheaper with Vanguard than anyplace else.
And, when you have bunches of money anyplace, trades get cheaper, advice and phone calls get answered faster and for me, it's a lot easier to pull everythiing together for the IRS each year. I really hope I didn't offend you on why accounts are in your name, for me I couldn't justify doing it although I've been the 100% breadwinner since the day we married many years ago.