Once you take the oath, you must exit and enter the US via a valid US passport. I have seen others successfully get an urgent passport same or next day when travel was scheduled.
This is exactly what the oath letter says about postponing the oath:
YOU MUST APPEAR FOR THIS APPOINTMENT - However, if you are under self-isolation or quarantine, are ill, have any symptoms of illness or are at heightened risk due to age or an underlying health condition and would like to reschedule your appointment, call the U.S. Citizenship and Immigration Services (USCIS) Contact Center at 1-800-375-5283 (TTY 1-800-767-1833) as soon as possible to reschedule your appointment. There is no penalty for requesting that your appointment be rescheduled.
COVID-19 Safety Precautions - To ensure the health and safety of all who enter USCIS facilities, you must take the following safety precautions when arriving for your appointment:
• DO NOT arrive more than 30 minutes prior to your appointment time. You will not be permitted entry into the office until 30 minutes before your appointment.
• Check www.cdc.gov for the county COVID-19 Community Level where you will appear for your appointment to understand the prevention steps for that location.
• Follow local USCIS guidance while inside USCIS facilities.
• You may have to answer health screening questions before entering.
• Bring a black or blue ink pen with you to your appointment.
Who should come with you? - You may be limited in who may attend your appointment with you in person.
• If you do not speak English fluently and are eligible to take the appointment in a language other than English, you should arrange to have an interpreter come with you to the appointment or be available via phone. If you need a Sign Language Interpreter or Certified Deaf Interpreter, call the USCIS Contact Center at 1-800-375-5283 as soon as possible.
• Your attorney or authorized representative may come with you to the appointment or be available via phone.
• If you have a disability and have an individual who assists you, that individual may come with you.
The naturalization ceremony is a solemn and meaningful event. USCIS asks that you dress in proper attire to respect the dignity of this event. If you cannot come to this ceremony, for a reason other than noted above, return this notice immediately with a written explanation on why you cannot attend to the office with jurisdiction over your naturalization case.
To find the correct office with jurisdiction over your naturalization case, visit the following website for more information: www.uscis.gov/about-us/find-uscis-office. You will then receive an appointment for a ceremony at a later date. If you are in the military, you may contact the USCIS Military Help Line for assistance, at 877-247-4645. To request a disability accommodation, go to www.uscis.gov/accommodations or call the USCIS Contact Center at 1-800-375-5283 (TTY: 1-800-767-1833) as soon as possible. For more information, visit www.uscis.gov/accommodationsinfo.