Is it better for a financially capable woman to pay for her 'Umrah expenses herself, or to ask her husband to pay for them, given that he does not object?

It is better for one who intends to perform Umrah (definition) to do so with their own money, out of a desire for reward. However, there is no harm in performing Umrah at the husband's expense. The Umrah will be valid if its conditions, pillars, and obligations are fulfilled. The husband will be rewarded for assisting you in an act of obedience. Performing the obligation of Hajj or Umrah at someone else's expense does not affect its validity, as long as its conditions, pillars, and obligations are fulfilled.