Technically. Zero. Is just an image source change.
If you're hiring someone then whatever they charge per hour x 1 hour lol.

Good luck

As Humberto stated, it should be easy; but depending on the complexity of the design, and how well it is implemented in the application, it could be longer: the worse the implementation (more probable for lower quality apps), the longer it will take.

Therefore, if the app itself is well-designed and follows best practices, the cost should be relatively low at about an hour or two.

However, this does not take into account ancillary work needed to re-publish the new app, which itself could take an hour, two, or more, depending on the issues that may arise.

It depends.

if minor branding changes mean = changing the logo, putting new labels then its not a job of more than couple of hours (or even lesser than that).

If minor branding = logo change, change of whole skin, layout then it can be a little longer job.

It also depends upon what kind of contract you have with the App developer, like if they cover this "white labeling part" already in the cost or its a new demand from your side.

The cost to white label an app with only minor branding changes can vary based on several factors, including the complexity of the branding changes and the developer's rates. Generally, since no structural code changes are needed, the cost should be relatively low compared to full app development. For a detailed breakdown of outsourcing app development costs and considerations, I recommend checking out this article: https://www.cleveroad.com/blog/outsource-app-development-cost/. It provides valuable insights into various factors that can influence pricing.