Yes copper sulphate solution can be stirred with silver spoon. This because the reduction potential of silver is more than copper.
Reduction potential of Cu2+ + 2e- --> Cu is 0.34
Reduction potential of Ag+ + e- --> Ag is 0.80
So copper will preferably undergo oxidation in preferance to silver and silver will always try to undergo reduction. So silver cannot undergo oxidative decomposition from silver spoon. It can be used to take copper sulphate. But Zinc cannot be used like this because the reduction potential of zinc is negative and it can easily undergo oxidation making the copper to reduce from the solution. .