Best orientation for CPU blower/cooler in 1U chassis
Solution 1:
All airflow in rack mountable hardware should take air in from the front and blow it out of the back. Neither of your proposed orientations are ideal. I wouldn't even run a normal PC without at least one case fan, never mind a 1U server.
You should monitor the temps with speed fan or something similar if you're unsure whether or not a single fan is adequate. In all likelihood, it won't be.
Solution 2:
Does the power supply at least have a fan? I hope so. If this is the case, then your best bet would be to blow hot air towards the PSU, which will (hopefully) blow it out of the chassis.
I agree with others, though: without case fans, airflow will very likely be too small to replace the hot air which will build up inside the chassis.
Solution 3:
YOu will overheat. The orientation does not matter- you NEED fans in the case, or the air gets stuck in it. 1u is very small for natural air flow, esepcially given that there is no way for the heat to get out on top.
Sorry, this may work for a low power CPU that does not require active cooling, but one that requires a blower.... you just kill the harware through environmental overheating.