Can I use a zip tie to replace the pin?

Jordan Chapman having seen your other Q&A's, it sounds like you are really wrestling with this. Let's face it, those standoffs are pretty hard to come by. No, you don't want metal screws. Reason for that is, because you may just overtorque those and pull them right through your board. You could use nylon screws but sounds like you are having difficulty sourcing those as well. You did say you have two of the four pins. Go ahead and use them on diagonal corners like @hellomacos suggested on another answer. Use your Zip ties ( very difficult to get the proper torque on those as well) on the other two ends. Be neat about it and be sensible when you apply those. No reason to yank to hard on those. Watch your board so as to not break that. Make sure that you properly apply some thermal paste between the processor and the heat sink. Once you got this all squared away and looking nice, fire up your Mini and keep monitoring the temperature. You will find out pretty quick if it is over heating or if it works. Can't use it as it is, can't get the pins, so might as well try something. Just be neat and tidy with your work. Is it a great repair? Nope. But for as long as it works for you and serves its purpose, it's okay by me :-)

Remember

REPAIR IS WAR ON ENTROPY