I would like to propose that Paul's encounter with a very rude viper on Melita (Acts 28:1-6) was not what Mark was referring to in Mark 16:18, "They shall take up serpents;". Here are a few reasons why:
1. Different gospel. The gospel referred to in Mark 16:15-20 is not the gospel of the grace of God, which Paul is proclaiming in Acts 13-28. Paul was not saved until Acts 9, so how could Mark 16 be referring to his gospel? The gospel in Mark 16 is the gospel of the kingdom, which was preached by John (Mt. 3), Christ (Mt. 4-9), the twelve (Mt. 10), and the seventy (Luke 10) when Christ was on earth, but also after his ascension. Peter knows nothing of the gospel of grace nor of the body of Christ, and his preaching about the cross in Acts 2 is in the context of a nation crucifying its king and needing to repent of that deed to receive their promised kingdom. When the leaders of Israel reject the re-offer of the kingdom (Acts 3-7), God sets the nation of Israel aside until the rapture (Rom. 9-11) and calls out Paul to begin building the body of Christ through the gospel (1 Cor. 3:10, Eph. 3:6, etc.). For further study, consult the Berean Bible Society, Dave Reese (website) or Peter Ruckman (Acts commentary). So you have a different gospel context in Acts 28 than you do in Mark 16, where taking up serpents is mentioned.
2. Different circumstances. In Mark 16:18, the text says "take up serpents," like picking them up. Remember Moses taking up a serpent in Ex. 4:1-5? It didn't take him by surprise and bite him. He reached forth and grabbed it by the tail ("Resist the devil, and he will flee from you"--Jas. 4:7b). In Acts 28, Paul is surprised, bitten, and shakes the viper off into the fire. Not the same circumstances as in Mark 16:18, which seems intentional. So snake handling is a kingdom sign, since snakes will be handled in the Messianic kingdom (Isaiah 11:8--"put his hand on"...). What a book we have in our hands, beloved!
3. Different audience. Paul's miraculous survival in the Melita incident is not a kingdom sign, but a sign to convert the barbarous, heathen people of Melita, since God also used signs to convert Gentiles during the Acts period (Rom. 15:18-19). Paul took his gospel "to the Jew first" during the Acts period (Rom. 1:16), but once the Jews had rejected his message in Asia (Acts 13:46), Europe (Acts 18:6), and Rome, the capital of the world (Acts 28:28), their special gospel privileges, including signs, concluded, and the gospel now went to all men, including the Jews, without distinction. Jewish missions do not have precedence over Gentile missions after Acts 28, since Rom. 1:16 apply to the Acts period, not today.
Things that are different are not the same, and even snakes need to be "rightly divided" :) (2 Tim. 2:15).