How much money is wire transferred every year worldwide? Estimates are fine.
If you're just trying to understand the volume of electronic transactions generally to an order of magnitude, it's in the quadrillions of dollars per year. According to this document from the US Treasury, SWIFT handles about \$5 trillion per day, or given about 250 business days per year, about \$1.25 quadrillion dollars a year.
Similarly, CHIPS handles about \$400 trillion per year, and Fedwire handles around \$900 trillion per year (most of both of these arise out of SWIFT messages). These transactions make up a large fraction of electronic transactions in the world, so it's safe to assume that the global total isn't much more than a few quadrillion dollars a year.
SWIFT payment message volumes are usually around 11.5 million per day, giving an average payment size of around \$45,000— though if one considers the structure of the payments system, it's evident that there's a very wide distribution of payments sizes, so this average isn't particularly representative.