Global searching can be turned off using the option searching = FALSE, and you may also disable searching for individual columns using the option searchable in columnDefs, e.g. we disable searching for the first and third column:

library(DT)
iris2 = iris[46:55, ]
datatable(
  iris2, filter = 'top',
  options = list(
    columnDefs = list(list(targets = c(1, 3), searchable = FALSE)),
    pageLength = 5
  )
)