can I use regex to replace spaces with underscores only in specific capture strings?

I would like to turn spaces into underscores in certain phrases for a regex find and replace. For example I would like this:

If you are going to the fair a trader there will offer you a fair price

into

If you are going to the_fair a_trader there will offer_you a fair price

I know how to capture these specific strings in various ways

e.g.

• (the fair)|(a trader)|(offer you)
• (the)(\s)(fair)|(a)(\s)(trader)|(offer)(\s)(you)

etc.

but I don't know how to handle the numbering of the capture groups so that the same replacement (space to underscore) will happen to any of them.

I attempted:

1.

• FIND: (the)(?:\s)(fair)|(a)(?:\s)(trader)|(offer)(?:\s)(you)
• REPLACE: $1_$2
• RESULT: If you are going to the_fair _ there will _ a fair price

• FIND: (the|a|offer)(?:\s)(fair|trader|you)
• REPLACE: $1_$2
• RESULT: If you are going to the_fair a_trader there will offer_you a_fair price

I'm not sure what else to try. Sorry if I'm not expressing my question right; I'm very new to this

• Ctrl+H
• Find what: (?<=the)\h+(?=fair)|(?<=a)\h+(?=trader)|(?<=offer)\h+(?=you)
• Replace with: _
• TICK Match case
• TICK Wrap around
• Search Mode Regular expression
• Replace all

Explanation:

    (?<=the)        # positive lookbehind, make sure we have "the" before
    \h+             # horizontal spaces
    (?=fair)        # positive lookahead, make sure we have "fair" after
|               # OR
    (?<=a)          # positive lookbehind, make sure we have "a" before
    \h+             # horizontal spaces
    (?=trader)      # positive lookahead, make sure we have "trader" after
|               # OR
    (?<=offer)      # positive lookbehind, make sure we have "ofer" before
    \h+             # horizontal spaces
    (?=you)         # positive lookahead, make sure we have "you" after

Screenshot (before):

Screenshot (after):

Another option if lookarounds are not supported:

• Ctrl+H
• Find what: (the)\s+(fair)|(a)\s+(trader)|(offer)\s+(you)
• Replace with: $1$3$5_$2$4$6
• TICK Match case
• TICK Wrap around
• Search Mode Regular expression
• Replace all

Explanation:

    (the)           # group 1
    \s+             # spaces 
    (fair)          # group 2
|               # OR
    (a)             # group 3
    \s+             # spaces 
    (trader)        # group 4
|               # OR
    (offer)         # group 5
    \s+             # spaces 
    (you)           # group 6

Screenshot (after):