If I'm reading OP correctly, they are looking for a way to be reimbursed in cash for using their own limited voucher credit. I suspect most companies would frown heavily on that, to the point of considering it fraudulent.

If this is a relocation for a current company, and the credit is from a previous business trip (that was reimbursed), then using the credit for the trip makes sense, and you'd be reimbursed for the additional cash cost.

If the credit is from a personal trip, best not to use it at all for this business trip. Save it for another personal trip.