If you are refinancing with the same lender it shouldn't make a huge difference to them. They know you have been making on-time payments for years. Their big concern is gross income, and obligations. Voluntary contributions to a 401(k) are easily stopped or modified. If the money being sent to the 401(k) was to payoff a 401(k) loan that would be another matter.
If you are refinancing with a new lender they may need an explanation. They can see that you have an existing loan, and your credit history doesn't show any adverse information regarding the loan, but they can't see if there were any unreported issues. Again they should not care about voluntary contributions.
Many years ago it could take months to change your contribution amount. With the first 401(k) program I was in you had to have the paperwork in the office several states away prior to the first of the month before the quarter ended. In other words to change it starting in January you had to submit the paperwork in November or the change would have to wait until April. Years later, after we switched to an online method that could change with every paycheck, one lender for a car loan thought the 401(k) contribution was locked in for a year. They initially denied the loan because they treated the contribution as if it was a loan. Nobody else has ever mentioned it despite several loans since then, including refinances.
That is always the strange things about 401(k) contributions and getting loan approval. If they do care about the size of the voluntary contributions, they also have to realize that you could lower them before applying and then raise them after the loan closes.
Should I apply, or should I wait?
While waiting for a month or two would remove the issue from their view entirely when they ask for the last couple of paychecks; I would not be concerned with it especially if you can clearly afford the new payment.
I also don't want to apply repeatedly because every application is a
hard credit pull.
The good news is that multiple hard pulls in a short period of time are considered a single hard inquiry because the model assumes that you are searching for the best deal. Though each application can cost you time and money.