Is it legal for a shareholder who receives no wages from company A to receive a reimbursement for business travel costs from company A in United States? Shareholder pocketed zero dollars of the reimbursement. Shareholders receive wages from another business B unrelated to A.
If I do some business travel for your company then I send you a bill for my working time and my expenses, and I expect it to be paid. If your shareholder does some business travel for your company, they can do the same. If they don't charge you for the working time, good for your company.
Just expect the IRS to look at this bill more carefully than usual to make sure this is not in reality a dividend payment. For example, if the business travel was "two weeks in a five star hotel in Hawaii, all expenses paid", that wouldn't look quite right and cause trouble for both of you.
PS: Cost of travelling to a company’s share holder meeting is not a business expense.