Per the rules, the DM has quite a bit of leeway in assigning mods to the die roll for any check. That's the key (and has always been the key) to the matter of making an ability check for something "outside the box" of codified skills and abilities.
Since no standard penalty for non proficiency is listed in the section on that optional rule, it is worth looking at the weapon non-proficiency penalty in Table 34, where non-proficiency penalties range from -2 to -5. With that range in mind, it would be consistent to assign a standard -3 or -4 penalty for a non proficient skill/undertaking, use the same ability base (Wisdom/Dex/Int, etc) as non weapon proficiencies, and then follow the usual process for an ability check based on the roll. Your initial idea of a -6 is just as valid.
The process in Ch 5 of the 2e PHB addressing non-weapon proficiencies (pg 113 - 117) would be a rational way to resolve those situations:
Consult tables 37 and 38 to find the ability score linked to that non-weapon proficiency (Int/Con/Wis, etc.) and for any + or - to the roll.
You add no further points. This give you the adjusted ability score before the roll.
- Roll a d20.
If the roll is equal to or less than the character's adjusted ability
score, the character accomplished what he was trying to do. If the
roll is greater than the character's ability score, the character
fails at the task. (A roll of 20 always fails.) The DM determines
what effects, if any, accompany failure. Of course, to use a
proficiency, the character must have any tools and materials needed to
do the job. Then add or subtract any mod the DM assigns based on the
conditions at the time.
To use your fishing example.
Cleric Festus has a Wisdom of 15 and wants to go Fishing(but lacks proficiency).
From Table 37 we see Fishing / Wisdom / -1
- Festus has an adjusted Wisdom of 14 (You the DM assign a -3 since he's non proficient, so he's adjusted to 11)
- If Festus rolls a 11 or less, he successfully fishes
- On a 12 or greater, he does not.
The DM could further add or subtract to the adjustment depending upon the weather, freshness of bait, excellence of the fishing pole, or whatever else the DM sees as a fair modification to that roll.
FWIW, if you are the DM this is what you have to decide: is it important to have a standard deduction for these ability checks, or should you just adjudicate it at the time? (From your question I'd offer that the former is your case). My play in the 1e and 2e eras, both as DM and as player, it was far more often the latter. We tended to leave the stuff on tables for the tasks on tables. What we usually did was that the DM and players would indulge in a bit of back and forth interaction/discussion for doing out of the box or non-standard things. This is the standard template for D&D play regardless of edition:
DM: Here's the situation
Player: Here's what I want to do
DM: (with or without die rolls) Here's what happened.
Doing that keeps play moving and also, due to the mini brain storming sessions that these entail, often raise a new or improved idea/situation/process in so doing.
Depending upon which optional rule books you use in your campaign ...
From the Players Option (Skills and Powers), Chapter 6, the tone is that it is very much up to the DM to decide what non-proficient skill he'll allow a player attempt a success at. Under the heading Use of Proficiencies by Nonproficient Characters ...
In general, characters will not be able to perform a task unless they have some level of proficiency in it. However, the DM can allow non-proficient adventurers to attempt proficiency tasks, under a few circumstances. In general, the tasks performed must be very simple, and the character will not be able to perform them very well ...
An example is given:
A non swimmer who falls in the water might be allowed to make a swimming proficiency check ... Note that this would be an automatic success for any character with the swimming proficiency.