If you want to make it even shorter, how about getting rid of the extraneous $d:

s;;5776?12321=10609=9409:12100;;s;\d*;push@_,$&;eg;warn chr sqrt,$/for
+@_
[download]

And, for that matter, you can trim it a fair bit further by just applying the function chr(sqrt(x)) directly to the capture, thereby avoiding the use of @_ entirely:

s;;5776?12321=10609=9409:12100;;s;\d*;warn+chr+sqrt$&,$/;eg
[download]

(I added the two '+' signs, as I think it looks better without any whitespace).