In the hotels in which I worked, the requirement of presenting a credit card was waived for anyone who had their room/tax being paid via direct bill. We simply blocked any incidental charges. In the unlikely event that there was room damage, we always could track down the guest via the employer.

To OP Max:
First, ignore the snide comment about your credit limit. It was not appropriate in this "flame-free forum where all FlyerTalkers can seek answers and advice without fear of unfriendly responses".

Second, it's a great idea to contact the hotel prior to your arrival. Call the main hotel number (not the toll-free reservations line) during normal business hours and ask to speak to the "on-site Reservations Manager". Explain your situation. Chances are very good that the problem will be a non-issue for the hotel. Be sure to write down the name of the person with which you spoke.

Note: The credit card authorization issue is a bit of a gray area. Where I worked, all pre-arrival questions were directed to the Reservations Department. In some hotels, however, that would be a question for the Front Desk. So, don't be alarmed if you get transferred to a different person.