If a limpet gets hit in combat there is a chance it will be destroyed (nearly 100% it seems) so it is a calculated risk to enter combat while a limpet is repairing. If I have lots of limpets left I do as you suggest. If not I get out and stay out of combat till repairing is complete.
Repairing in NHSS
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In NHSSs going FAO and boosting is the only option for repairing as all Scouts will be agro all the time. In that case I boost clear of Scout weapon fire and just as the last boost starts to initially decay in speed I fire a decontamination limpet. Limpet should attach almost immediately, if not I slow down till it does then boost clear of Scout fire again till it is done. Make sure to have enough spacing margin to accommodate this slow down when needed. If not boosting try go be flying in FAO "backwards" for decontamination and "forward" for repair as it seems to improve their chances to directly attach. These limpets can be very fussy about attaching on smaller ships but this help me a lot.
Avoiding caustic damage
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However my preference is to shoot down caustic missiles with this Vulture build and avoid decontamination as much as possible. It depends on luck a bit but if not hit within the first few seconds it is very likely to work. When missile launch is announced go FAO and boost, pips to 2/4/0, selecting highest priority target (h key on my KB/M settings) should target missile, then fire multis and keep boosting, keep/position missile above and behind (multis can't fire directly behind) when it gets within 1Km, and keep boosting. If missile gets within a few hundred meters multis will usually take it out, otherwise if missile never gets that close it will eventually destruct on it's own.
This Vulture will FAO boost at about 380, Scouts will fly at about 280, and missiles about 340. However, if Inciter special attack boosts their speeds this Vulture will not outrun either, even when full FAO boosting. In that case be prepared to jump out of instance.
There are lots of ways players suggest to use the Shutdown Field Neutralizer (SFN) but it needs to
fire/charge prior to the Shutdown Field arriving and stay active (fire button pressed) for the entire time the Shutdown Field passes over the ship to succeed. It needs to be mapped to a fire group and fired/charged just prior to the Shutdown Field reaching your ship. It will quickly deplete the SYS Power Distributor (PD) energy and the time it is active depends on how much power your PD can supply. When the PD is empty it will automatically cut off. If you accidentally press the button for even an instant there is a 10 second cool down before it can be used again so don't fat finger it just before needing it, I know this only too well.
How I use SFN and observations
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When I need to leave a AX CZ I go pips 4/2/0, FAO boost, then start listening for approaching Shutdown Field. The approaching Interceptor and approaching Shutdown Field sound similar to me but the Interceptor's sound ends with a boom. Once I hear the boom the next sound that has that ramping up sound will be the Shutdown Field. I wait for it to ramp up a bit then fire the SFN. If you have visual line of sight to Interceptor watch for the pulse glow then watch the Shutdown Field approach and time it that way. Consider un-mapping the deploy weapons on firing button press to avoid deploying weapons when trying to flee, SFN and repair limpets can both be fired with weapons retracted.
Be aware that when using the SFN the Interceptors will almost always agro on your ship as opposed to doing FAO drifting where they will usually only agro when near your ship. This is because when your ship goes cold the bugs have a hard time tracking it, when your ship doesn't shut down they usually track your ship as first priority.
The problems I have with other SFN methods is that the incoming energy surge message doesn't always play because of bugs and the count 3 seconds method relies on the Interceptors being a "nominal" distance, which they are not. Sometimes they spawn so far away the field never arrives and other times they literally crash into my ship as they materialize and send it spinning through space.
There is a bug where FSD engaging will cancel SFN. If the Shutdown Field hits at that moment the ship will jump but still shutdown and never reboot. The only way to fix it that I know is to exit to menu and restart.