The most common and most likely answer to this crossword clue is the 8 letter word SHADIEST
I've seen this crossword clue in The Times
S
H
A
D
I
E
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T
Buddy explains!

The straight part
We know that "most dodgy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case most dodgy = shadiest.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SHADIEST mean?
SHADIEST adjective- Abounding in shades.
- Causing shade.
- Overspread with shade; sheltered from the glare of light or sultry heat.
- Not trustworthy; disreputable.
- Mean, cruel.