If a printer prefers their own profile, they can do a conversion from a known profile to their in house profile instead of assigning one.
In fact I don't think any printer wants "mystery meat" (untagged images) where they have no idea what profile you did the work on.
However if your printer insists on untagged images, a simple way is to open the source PNG, File > Export > Save for Web
And set the PNG export to "no color management", then save the exported file as tiff.
You definitely want your color policy for Grayscale turned off before you do.
What file format are you saving to?
You should be able to use edit/assign profile to apply the “don’t colour manage” option…
There is a subtle difference indicated in the document title bar…
Converting a untagged RGB to grayscale effectively tags the working grayscale to the image:
If you then use edit/assign profile/don’t colour manage:
Notice the # hash mark next to the bits per channel indicator?
Also, the lower left area of the application has a readout where you can show colour profile, document sizes etc. With colour management off on an image, you should see this:
You should be able to deselect the colour profile when saving the image…
What I did is to batch convert rgb jpegs and pngs to rgb tiffs. Then convert to greyscale. Then batch strip out the greyscale dot gain profile, if there was one. But, it didn't work with the pngs that had been converted. No hashtags anywhere. And the printer did say they preferred no profile, but maybe I don't really understand what;'s going on. So, they are tiffs... but I don't know why these particular ones didn't work.