A compressor will probably bring out more of the hand, string, and fret noises, not hide them. (If you want an explanation why, ask and i'll gladly reply.)
First i'd
listen to some of Geddy's isolated bass tracks and see if they're actually as noisy as yours or not. Great mixes hide a lot of instrument noise. So you'd be surprised what you hear in isolated tracks. His playing isn't pristine and silent, but there's not a TON of noise neither. If you're not hearing noise on Geddy's track, it most likely never was there in the first place, not recorded & removed or hidden.
Then get a proper setup from a professional. It's a cliche suggestion on TB, i know, but i'd say start with a proper setup from a tech/luthier who can set your bass up for your playing style, to make less playing noises. It'll probably include raising the action a touch. They should be able to get the action higher without making feel too high. Higher action = cleaner, especially if you play aggressively.
After the setup, controlling non-musical hand, string, and fret noises is a technique thing. Start experimenting with modifications to your aggressive style. Plucking angles, muting techniques, etc etc. Find ways to play aggressively without also causing noise. And maybe pull back on how aggressive you're playing just a touch and let a kiss more overdrive and high-mids "aggressive-up" the track.
Last on the list would be to try to remove the noise using audio processing.
- Unwanted noise in the transients of notes can be tamed a bit with compression, especially if it's making the transients too hot: fast release, fast attack, 4:1 ratio. Just kiss the compressor for the transient but not the rest of the note. You're basically just compressing out any noise that's louder than the note before the body of the note starts.
- Noises in the notes may be addressed a bit with EQ if it's happening in a certain frequency range, but be careful that you're not also EQing usefull bass information. EQing can also be tricky because sometimes noise is broad-spectrum so you can't just negative-EQ a frequency because it's across all of them.
- Noises in between notes can be reduced or removed with a gate or expander. But, make the gate/expander transparent. We shouldn't hear it engaging and releasing between notes and it shouldn't be cutting off your notes at all. Getting a transparent gate/expander in a mix is tricky.
- Plugins like the iZotope RX can do noise removal. It could also very well change the tone of your bass. So use it carefully.
- None of this will actually remove the noise, only hopefully get them down to a manageable level. Once it's in there, you can't really get it out. So, it's best to put as little of it on there.