I expect every country has its own rules and guidelines governing expense reimbursement, though from your point of view, as a U.S. payer (and assuming the travel expenses in question are in support of your business), I’m not sure that you must do more than observe IRS accountable plan rules on the U.S. side; and that each of the payees would individually be responsible for appropriate reporting (and documentation) on their side. That could mean in some countries that they need to hold onto original receipts, but the IRS accepts electronic records, so that should not present an issue on the documentation side. (Of course you want to have appropriate management review/authorization for the travel expenses in place.)
Here are comments from one of our global experts:
Every country does have rules about T&E, such as amount thresholds for receipts, what is considered a T&E receipt, where receipts need to be kept, how long to keep receipts, and whether the reimbursement is perceived as personal income. For example, Puerto Rico requires the T&E amount to be sent on a 1099 and the employee has to provide the government with original receipts at year-end tax time. Italy does not allow original receipts to leave the country...and penalties could include jail time for executives!
Since you have such a large number of countries you are supporting, we would suggest you consider hiring a VAT recovery group like Meridian, which focuses on T&E VAT recovery, and will know what each country requires and can keep you updated. Meridian or other such expert should be able to help you set up and review the existing records to ensure you are compliant.