How to keep fine detail when removing background

We recently lost our dog, but received several paw prints from the vet.  I am trying to use these  to make ornaments but cannot remove the background without losing some of his paw print detail.  i have saved it to png.  i have tried selecting by color, but there are different color shades in the image.  i have tried to use the different selection tools, but it just doesn't capture everything.  And i really want to capture every spec of detail.  I am more familiar with photoshop (2024) but also have illustrator (2024).  Please help!  Really would like to make these keepsakes for my kids, as best as possible!