A lot of gear uses a "floating" ground (better called a neutral). With out knowing how your gear is wired, it is hard to say if using the grounding lug on your preamp is "safe." I would expect any decent phono preamp's TT ground lug to be "lifted" from earth to avoid common mode interference and not be connected directly to earth. Your amps should be fine with discharging the static, but a lot of gear leaves out important fail safes in order to keep the signal pure. That said, class A amps are pretty much immune to this type of abuse.
No idea about how a static pop might affect a cartridge.
If you are worried about it, you need the same hand that lifts the cartridge to be grounded. You can buy a grounding cord. It looks like a 3prong extension cord, but it only has the earth wire, and either an alligator clip or ring lug on the other end. Plug it into the same outlet that the TT is plugged into, pick up the lug to ground yourself, and move the TT arm while holding the lug. wintery dry hands also do not conduct as well as healthy moist skin, so a bit of lotion (or just lick your palm). It might have the bonus to bringing less dust onto the record as well.
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