Radiator replacement question Options

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Bit the bullet and decided to try to resurrect my Base Level 94 Celica ST 1.8L with manual transmission. It has been unable to start for over a year and a car buff friend stopped by and assured me he would help me pull the engine and get me through the problems of rebuilding it's 7AFE.

So, the engine bay is empty, the garage is full of mostly washed parts, the engine block in on an engine stand, I have a rebuilt head, and I am faced with the following problem about the radiator:

What caused her to shut down was an overheating event which messed the head gasket, warped the head so it could not be repaired, and blew a hole in the RADIATOR.

It just so happens that a couple of years ago when I was redoing her suspension, brakes and wheel bearings all round, I needed a front steering knuckle and found one on a Celica at a local junk yard. At that time I also ripped off that Celica's decent looking radiator and brought it home where it has been stored ever since.

My Celica's transmission is manual. Its radiator is different than the one I got at the junk yard, which is for an automatic transmission. There is no identifying information on the junkyard radiator, and I do not recall what Celica it came from, but maybe 1995, just guessing. I moved the two fans from my old radiator and was easily able to mount them on the junkyard radiator. The only way I know the two radiators are different is that 1) my radiator core is about 5/8" deep, while the junkyard radiator core is 1" deep, and there are two teats on the bottom of the junkyard radiator (for automatic transmission fluid) that are not on my radiator.

All that said, the QUESTION:

Would it be ok to use the junkyard automatic transmission made for radiator in my Celica that used a radiator made for only for a manual transmission? Would it cool my engine properly? Are their any snakes laying in the direction of my thinking?

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I would boil just the water, then pour the flush and water in behind it into the radiator since that'll get it mixed well enough and then shaking the radiator will get it the rest of the way.

If you're wanting to clean the block the only thing I'd know to do is use pipe cleaners, outside of having it dipped anyway. Another option would be to wait until everything is in the car and running then do a flush that way to get the whole system. I think machine shops are becoming a thing of the past outside of specialty shops, these days they don't rebuild engines when a car blows one under warranty they just replace the whole thing.