The best replacement for second is secondly.

The best alternatives to second are rated as following:
★★★★★  secondly
★★★★  third person
★★  2nd
★★  millisecond
★★  junior
★  miles per hour
★  second
★  another minute
★  bytes per second
  blur
  first pregnancy
  mph
  first degree murder
  deuxieme
  burnout paradise
  first focal plane
  bits per second
  60 frames per second
  third degree murder
  frames per second

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Speaking about second, one probably shouldn't forget about none.

Other search terms related to second and their ratings are:
★★★★★ none
★ arms in second
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Google Trends

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second
secondly
third person