Since your are not expected to pay the bill in full you would not be hit with the full 10K in the debt to income rations . My understanding of CC is that you would be required to pay 2% of the 10K or about 200 that would get factored into your monthly ratio’s.
What typically hurts is if the credit line were 10K and you were using the full 10K, this would then show up as 100% usae which would reflect a high amount of risk and lower the credit score. If you ahve 50 K of credit and you are using 10K it is only reflecting 20% which is very conservative and considered normal. This is why you ahve a vry good credit score.
Best be is to simply order a copy of your credit score before searching for credit.