There is a LOT you can do in Melee just by thinking. Think about what options you would use in what situations. How would your opponents think to counter those options? What would the response to that be?
Example line of thought: You're Marth and your opponent is Fox. What is your win condition? Start a combo and get Fox offstage. You're both dashing back and forth in neutral on stage. What's the best way to start a combo? > Grab. Winning tactic: attempt to grab.
So then you run up to Fox and you try to grab him. Now what does he do in response? Imagine yourself in the opponent's position. He could dash back, forcing you to whiff your grab. He could throw out an attack to stuff your approach. He could spotdodge or roll expecting the grab. All of these options will beat you if you just try to run forward and grab.
So now what can you do? Perhaps instead of running up and grabbing, you run into his space and immediately shield. If he dashes back, you have now taken stage control. If he throws out an attack, you can wait for a hole in his pressure and punish him. If he rolls or spotdodges, you can now wavedash out of shield and apply pressure or get a grab. You now have an advantage.
Of course, now Fox will have to think about ways to beat run up shield. Perhaps he will run up and initiate a shine premptively, or perhaps he will retreat to ledge and stall for an opening.
This is endless. The way players respond and adapt to each other's actions forms the core of every fighting game and even every sport on the planet. Melee is a game of endless adaptation, and you can improve a LOT just by going through mental drills like this in your head. Whichever player adapts the fastest wins.
Tech skill is nice and all, but it's only an extension of your tools. Practice it, but always prioritize practicing thinking. I hope this wasn't too confusing. Best of luck!