It shouldn't matter which way round you connect it up, it will just mean the oil flows one way through the cooler, or the other way. 60lbs is fairly high pressure, but not uncommon when cold, and your pipes should be able to deal with it.
I have just finished an oil cooler install myself actually, with my hoses attached to barbed fittings with 2 worm drive clamps on each connection (I will replace the clamps with some full circle bolt type ones when I find some). I was worried about them leaking but they are not leaking at all. I did use a very thin smear of high-temp silicone sealant on the sealing surfaces, but because the of the type of fittings, these sealing surfaces are never threads. I am not sure what the best method to seal threads is.
Here is a picture of my installation:
