Best way to handle $10k in credit card with with Costco (Citi visa card)?

I inherited some debt when I got married. My wife and I handle our income shared. So we have one main bank account where all of our income goes to. I personally prefer it this way. Our income is our money, so if I get a raise (or she does) it naturally benefits both of us. That is a personal preference that I know not everyone does.

This also means that once married, her debt, became our debt. It impacts the both of us. We did just pay off a 2-3k credit card connected to Amazon.

Prior to us meeting she had gotten into some debt during COVID times. The debt does not reflect on her normal spending habits. We are not adding to this debt and we are both good at making sure we are not over-spending. IDK why I feel the need to defend, that isn't the point.

The point is we now share 10k in Costco debt through Citi. I am currently working on getting access to it, but from what I understand the interest can be as high as 25% which means we would be adding hundreds a month to our debt.

I am better at numbers then my wife, so I explained it to her that its like we are being charged at least $200 a month. So if she pays off $400 on the card, it really is just $200 off the total that month.

We have about $15k in savings, but we don't want to just lose all of that. I have also already discussed paying it all off at once and that wasn't agreed on.

However, I was thinking that maybe I could transfer that debt to my bank (Bank of America). Not really posting to discuss Bank company choices, more on if this could be a good idea.

I read that there is an initial transfer fee, but sometimes you can get a year or two or little to not interest? If so, then maybe that is the right decision?

$200 for two years is $4,800!

Even if a transfer feed was $1k (which I doubt) we would save thousands?
However I am thinking transfer would be closer to $300-$500?

Either way. Lets say a transfer would save us $4000 due to lower interest? We could easily cut that debt in half or even get rid of it in the next two years.

Am I missing something?

Is there maybe a better way to do this?