drop the guns you wont need them.
downgrade the power plant, the thrusters and the distributor, you wont be pulling much power, you dont generally need high grade thrusters when exploring, and you can disable the distributor altogether (when you downgrade the distributor make sure you can still boost dont downgrade past that).
you can safely downgrade the shields by a lot, I generally carry a class 3, again you wont be needing them except for trips in asteroid fields and when you return home to dock.
Bring the biggest fuel scoop you can, I am running a 6B and it does the job well. a 6C would work fine, a 6A would be slick, but is expensive. Id personally recommend doubling up on FMU and bringing at least one heat sink, two is better if you can fit them.
get kitted up and then disable the following:
shields, cargo hatch, sensors, distributor, any AFMU's and all but one heat sink.
then look at your power usage and see what PP is going to cover all of those and downgrade to it or one slightly larger, get an A grade of that class ideally to help with heat dispersal, or D class if you're still worried about mass.
just my .02 cents
EDIT: If you MUST bring guns, dont bring multicannons, you wont be able to reload them in the black.