With Wii Remote its a bit trickier with me :/
Thanks for all the help! I might post any questions I have later, but thanks!
If you're even halfway serious about playing Smash, and you posting here indicates you are, I'd switch to a different controller. I can understand not wanting to make the switch away from Remote+Nunchuk or such if you're not trying to get competitive, but Wii Remote just limits you far too much.
Also about your original question: The most important technique you should learn for approaching is dashdancing. SH NAir for example, depending on the distance, can connect faster than your opponent is able to react to your jump. What you usually do is react to the opponent starting an approach, but proper dashdancing makes it near impossible to know that you're about to go in before it's too late.
tl;dr: You don't have to always go in if you're going towards.
Next, against shielding: Learn to JC grab (jump and then grab before you leave the ground, this allows you to do your standing grab out of a dash/run). It's much less punishable than a dash grab and unreactable (unless your opponent expects it
and has a godly reaction time, maybe).
Further, if you NAir an opponent's shield and l-cancel it, jab them. Jab beats out many oos options and your opponent has to respect Jab 2, so mixing up between using Jab 2 (if they don't respect it) and not using it (if they do) is already okay shield pressure. You also don't always have to jab. If your opponent expects the jab and tries to wait it out, you can just grab them.
Transferring to using magnet and DJC FAir as your primary approach tools would be the next step (both are safe on shield, if you have a plan for what to do afterwards), but I don't think you'll be able to wd out of magnet or djc l-cancel FAir consistently with a Wiimote.
DJC PKF is probably your most reliable tool in the beginning. The only problem is that there's tons of counterplay to it that makes it a really fair projectile later and that you won't learn real fundamentals if you're used to being able to PKF->grab 95% of the time.
Also Badge with all this sick Lucas knowledge you're dropping I'd be keen to see some vids of you playing him.
I barely touched Lucas since 3.0. He feels really awkward with all the minuscle timing changes and I've also found other characters to better suit my play style. If I play Lucas nowadays it's purely on fundamentals without many character specific strategies or tech above DJC aerials (those thankfully didn't change). I only still post about Lucas because I have tons of knowledge from v1-3.0 and he's really fun to theorize about.