Is there a way it is normally done that wouldn't involve a lot of risk for me or a bunch of extra work?
This is the real question and the answer is no. The other answers go over the general reasons why you wouldn’t do this. As referred to in the other answers generally either the buyer arranges financing themselves at their bank or the dealer will help place a loan for the buyer; the dealer gets paid in full and doesn’t carry lending risk.
There’s a somewhat common business model in the US referred to as a “Buy-here, Pay-here” used car lot. These dealers typically have very old cars on the lot, for somewhat inflated prices, with loan terms that are utterly awful. They generally don’t really bother checking your credit, but will call an employer to verify you’re employed. And these companies aren’t car dealers as much they’re collection agencies. The way it works is someone with bad credit needs a car and can pay $50 every other week. You sell them a car worth about $1,500 for $2,500 but they’ll pay you $500 today plus $50 every other week for 3 years. Then you add them to your call list. If they don’t pay you check the gps tracker, you send a very scary looking person to go pick the car up and you put it back on sale. This works, ultimately, because you’re collecting on 20 cars (or whatever), not one. And no one is going to “Gone in 60 Seconds” you and put it in a container to another country to actually steal it from you because no one really cares that much about a miscellaneous 15 year old Nissan Sentra that’s in not great shape.
Really, the business isn’t about selling cars because you’ll sell the same car several times; it’s about creating the debt to collect then being very persistent in collecting then ultimately repossessing the car.
The question for you is would you lend this stranger $100? (Not even the $2,500 they’re asking to borrow.) And I mean lend in the true sense of the word, you fully intend to receive the money back and will pursue collection when the borrower inevitably has an emergency. And the answer is probably no. Almost everybody is bad at this part of lending, regardless of what the collateral to the loan is. Everything else is downstream from this, insurance, interest rate, borrower qualification, loan documentation, whatever. It doesn’t matter because the reality is you’re probably not ready pick up the phone and assert yourself in to a conflict with your unwilling borrower who doesn’t think they should pay you if the water pump broke or they got sick and couldn’t get to work this week; and that’s why you shouldn’t get yourself in the business of direct lending.
Buying a car is actually two transactions. One transaction is the price of the car, one transaction is the price of the money (the loan). This person wants you to become a bank, that’s why this is a bad idea. In your situation your buyer is requesting you give up possession and utility of your car and lend him $2,500; and you get no collateral apart from the car he will have legal possession of.
This question has basically nothing to do with whether you file a police report if your car doesn’t come back and you haven’t heard from your borrower (and no this is its own thing called “theft by conversion” and there’s very little the police can do when the person who is legally allowed to have the car just isn’t returning your phone calls, though depending on your jurisdiction you may have to file a police report to be legally in the clear to repossess the car procedurally.). Let the buyer arrange their own financing, and if there are no buyers at $2,500 lower the price a little. Taking $2,250 for the car is still an order of magnitude better than getting the first four payments from this person and nothing else.