Do you know your 'KVZ's?

Python 3, 140 133 124 123 bytes

d=*map(set,'AJK BCDEGPTVZ IY QU SXF MN H L O R W'.split()),
print([d[int(c,16)].pop()for c in'0111141620075581394131a421'])

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_{-1 byte, thanks to Jo King}

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Python 2, 174 170 158 bytes

from random import*
s=''
for c in'abbbbebHcaaLffObdRebdbWecb':s+=choice(list(set(('AJK BCDEGPTVZ IY QU SXF MN '+c).split()['abcdef'.find(c)])-set(s)))
print s

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05AB1E, 28 bytes

A.•¬=©ƶÓÄûkTVã”ØζÞ•Dás#€.rJ‡

Outputs as a single lowercase string.

Try it online or verify \$n\$ random outputs at once.

Explanation:

A                    # (a) Push the lowercase alphabet
 .•¬=©ƶÓÄûkTVã”ØζÞ•  # Push compressed string "ajk bcdegptvz iy qu sxf mn"
  Dá                 # (b) Duplicate it, and only keep the letters (removing the spaces)
    s#               # Swap to get the string again, and split it by spaces
      €.r            # Shuffle each substring randomly
         J           # (c) Join it back together to a single string
          ‡          # Transliterate all characters from (b) to (c) in string (a)
                     # (and output the result implicitly)

See this 05AB1E tip of mine (section How to compress strings not part of the dictionary?) to understand why .•¬=©ƶÓÄûkTVã”ØζÞ• is "ajk bcdegptvz iy qu sxf mn".

Ruby, 102 bytes

s=[*?A..?Z]*''
%w(AJK BCDEGPTVZ IY QU SXF MN).map{|e|a=e.chars.shuffle;s.gsub!(/[#{e}]/){a.pop}}
$><<s

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