I checked hte Journal of Forensic Science and it stated that there can be difficulties associated with lifting fingerprints from tape especially if one does not use the latest technology. Given that the gun involved was circa 1946, the technology back then was relatively primitive.

So, apparently tape generally and a "special" tape in particular could present fingerprint identification problems. But also consider that when Mike pulled the gun from behind the toilet he apparently had both his hands all over the gun.

"Generosity. That was my first mistake."
"Experience must be our only guide; reason may mislead us."
"Instagram is Twitter for people who can't read."