As Keen said: The problem is more with the airline and security than with immigration when you get there.
(You will probably get pulled out of the security line and ‘interrogated’ bc you are on a one way ticket- it’s a big red flag for security).
But I would use Nechomah’s trick if you have to and just buy and then cancel a ticket- that will take care of the airline but not of security- just keep your story simple, don’t lie and don’t let their questions confuse you.
If you are going to do that make sure A) that you get to the airport on time (early) so that you have time for them to give you a hard time/ buy the ticket etc, B) you have a credit card with enough credit on it so that you can afford to buy a (really expensive) non-discounted/business ticket (that you will later cancel) and C) you ask them exactly what you need to do in order to cancel the ticket.
G’luck
PS: let us know what happened- I’m interested to know.