Not sure about a mod, but it's easy enough to disable fatigue all by your lonesome.
Start by using Notepad to open the Basic.fg file in your 'SH3\data\Cfg' folder. Once you've got it open, use the CTRL-F (Find) function to quickly locate the '[FATIGUE_COEF]' section. It should look similar to this:
[FATIGUE_COEF]
;comp0 tower
RegularFactor00=0.001
SpecificFactor00=0.01
BadWeather0=0.02
;comp1 sonar/radio
RegularFactor10=0.001
RegularFactor11=0.001
SpecificFactor10=0.01
SpecificFactor11=0.01
BadWeather1=0.001
;comp2 command room
RegularFactor20=0.001
RegularFactor21=0.001
SpecificFactor20=0.01
SpecificFactor21=0.01
BadWeather2=0.001
;comp3 diesel
RegularFactor30=0.001
RegularFactor31=0.001
SpecificFactor30=0.01
SpecificFactor31=0.00075
BadWeather3=0.02
;comp4 electric
RegularFactor40=0.001
RegularFactor41=0.001
SpecificFactor40=0.00075
SpecificFactor41=0.01
BadWeather4=0.001
;comp5 bow torp
RegularFactor50=0.001
RegularFactor51=0.001
SpecificFactor50=0.045
SpecificFactor51=0.045
BadWeather5=0.02
;comp6 bow rest
SpecificFactor60=-0.0000003
SpecificFactor61=-0.0000003
;comp7 stern rest
SpecificFactor70=-0.0000003
SpecificFactor71=-0.0000003
;comp8 stern torp
RegularFactor80=0.01
RegularFactor81=0.01
SpecificFactor80=0.03
SpecificFactor81=0.04
BadWeather8=0.02
;comp9 deckgun
RegularFactor90=0.001
SpecificFactor90=0.05
BadWeather9=0.02
;comp10 flak
RegularFactor100=0.001
SpecificFactor100=0.05
BadWeather10=0.02
;comp 11 repair station
RegularFactor110=0.001
RegularFactor111=0.001
SpecificFactor110=0.02
SpecificFactor111=0.02
BadWeather11=0
This is where fatigue levels are set for every compartment on your boat. If you want to disable them, simply change all the levels to 0. Good luck, have fun and enjoy your new super crew!