I'm not sure what you're trying to accomplish. If you stop getting reimbursed for the travel expenses, but you still have to pay the expenses, then you are just making less money. You would pay less tax because your income would be lower. You would still deduct the travel as business expenses, but you would be paying them out of your own pocket instead of being reimbursed. You can only deduct what you actually paid.
Your client should be sending you a 1099-NEC for everything that they pay you, not just travel expenses. Normally they would send one 1099-NEC at the end of the year for the full total amount that they paid you during the year.
