Replace colors on two color image with faded edges?

Hi,

I am using Photoshop version 21.1.3.  I have a .png file with some simple symbols that are black on a white background.  Rather than consisting entirely of pixels that are either black or white, the edges of the symbols fade from pure black to pure white through shades of gray over a span of a pixel or two. 

I'd like to convert this image to cyan on a black background, but I would like to preserve the same fade around the edges (so that the edges will fade from pure cyan to pure black in the same way that the original symbols fade from black to white).

If anyone here can give me an idea how I can accomplish this, I would greatly appreciate it.

Just in case it is useful, I have attached the .png file I am working with.

Thanks in advance,

Paul