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for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

or the faster, thanks to Gilles' suggestion:

for file in /foo/*
    do
      if [ -f $file ]
      then
        tail +32c $file > $file.truncated && mv $file.truncated $file
      fi
    done

Note: Posix tail specify "-c +32" instead of "+32c" but Solaris default tail doesn't like it:

   $ /usr/bin/tail -c +32 /tmp/foo > /tmp/foo1
    tail: cannot open input

/usr/xpg4/bin/tail is fine with both syntaxes.

for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

or the faster, thanks to Gilles' suggestion:

for file in /foo/*
    do
      if [ -f $file ]
      then
        tail +32c $file > $file.truncated && mv $file.truncated $file
      fi
    done

Note: Posix tail specify "-c +32" instead of "+32c" but Solaris default tail doesn't like it:

   $ /usr/bin/tail -c +32 /tmp/foo > /tmp/foo1
    tail: cannot open input

/usr/xpg4/bin/tail is fine with both syntaxes.

If you want to keep the original file permissions, replace

... && mv "$file.truncated" "$file"

by

... && cat "$file.truncated" "$file" && rm "$file.truncated"

for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

or the faster, thanks to Gilles' suggestion:

for file in /foo/*
    do
      if [ -f $file ]
      then
        cut +32c $file > $file.truncated && mv $file.truncated $file
      fi
    done

Note: Posix cut specify "-c +32" instead of "+32c".

for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

or the faster, thanks to Gilles' suggestion:

for file in /foo/*
    do
      if [ -f $file ]
      then
        tail +32c $file > $file.truncated && mv $file.truncated $file
      fi
    done

Note: Posix tail specify "-c +32" instead of "+32c" but Solaris default tail doesn't like it:

   $ /usr/bin/tail -c +32 /tmp/foo > /tmp/foo1
    tail: cannot open input

/usr/xpg4/bin/tail is fine with both syntaxes.

for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

for file in /foo/*
do
  if [ -f "$file" ]
  then
    dd if="$file" of="$file.truncated" bs=31 skip=1 && mv "$file.truncated" "$file"
  fi
done

or the faster, thanks to Gilles' suggestion:

for file in /foo/*
    do
      if [ -f $file ]
      then
        cut +32c $file > $file.truncated && mv $file.truncated $file
      fi
    done

Note: Posix cut specify "-c +32" instead of "+32c".