Using a garden hose and a trigger spray nozzle, I have never had a failure in over 40 years of doing this.
That said, one of my moron employees....decided he was going to NOT follow directions, and used shop air and a suction hose to "blow" out a core.
He blew it out, alright....at 150PSI right out of the case!
I just hold the nozzle up to the heater hose nipple....not screwed into a hose on the nipple.
Back and forth, it will dislodge all the built-up garbage that has settled into the core.
I did my Jag....went from ZERO heat to quite comfortable for the lovely bride.
The 4PSI is cap release pressure.
Unless that core is toast, according to my radiator shop, cores and radiators handle MUCH more than that.
They generally test radiators (even my Flathead 4PSI ones) at something like 50 PSI.
I don't want to tell you what to do and have you blow it out....but, they will pressure flush it anyway, at a guaranteed higher than 4PSI.
The back-and-forth is what does the trick.
If you are concerned, keep the faucet cranked way down.