How to avoid metal chips entering the cavity when drilling / milling cavity holes?

Hello, my regards from everyone! I have acquired a Jaguar XJ40, in good condition, now after years I suspect that rust could be there. At least it wants to find out. I will drill holes according to the cavity plan (and at a few other places) and check them with an endoscope camera. Then depending on the condition, the corresponding measures such as rust removal, Mike Sanders grease and all the other products that are available. My chuck in the Bosch cordless screwdriver only goes up to 10mm, after that only a step drill is considered as a tool. Question: are there any lubricants or other products with which I can lubricate the drill/miller so that no metal chips can pour into the cavity during drilling or milling? Thank you in advance and best regards!