You should never be afraid to do anything, honestly. Any amount of hesitation almost always leads to failure. I would just recommend going with the best course of action at 100% and either have it work or fail. If something tells you to approach and they keep WDing back, don't begin hesitating when you want to approach. This will probably only make it WORSE. What you have to do is figure out how to make your approach work or close space so that they are forced to approach from a bad position (usually bad meaning on the ledge, on a platform, etc.).
Almost any situation that makes you afraid to do something usually just means you haven't been exposed to that situation enough. I would panic a lot more if I got grabbed by a Falcon than if I got grabbed by a Marth because I have 100x more Marth experience. Even if Marth has an obviously better punish game on spacies from grabs, I am PREPARED to handle those punishes. I would be unprepared vs. Falcon, and I have a lot more hesitation about DI the throw, how to tech, and how to DI/jump out of the follow-ups.
Since you are scared in the neutral game when they are DDing, it means you aren't sure how they will approach/what they will use to approach, and thus, aren't sure what to do about it. I see this a lot in newer players. They get kicked in the face trying to move. They start holding shield to avoid SHFFLs and begin getting grabbed. They begin spot dodging/rolling to avoid grabs and start getting caught by their opponent just DDing until they shield/spot dodge/roll. Then after 30 minutes of this they go "WTF I can't do anything!" lol Instead of trying to predict what someone will be doing 1-2 seconds in the future (which is impossible in Melee), you have to be proactive with your decisions. The two main choices you can do in neutral are:
1. Space yourself so that your opponent's approaches won't work, or
2. Approach in a way that protects you from their own spacing/defensive options.
DDing and WDing, being the two major forms of spacing/movement, are the core of both options. In order to approach successfully, you need use them to bait out reactions (WDing/DDing back is a reaction to closing space) and space attacks so that you don't get shield grabbed and are able to capitalize properly on successful hits. In order to protect yourself from approaches, you need to be able space yourself so that they think they can hit you, but they can't either because you spaced yourself out of their range, yourself within shield grab range, etc.
Obviously just viewing Melee within the scope of two options is dumb, but it's the general framework within which I view details, and it's more and more blended the better you get. If you watch for this when it's two bad players playing, it's always SUPER obvious who is approaching and who is defending. With good players, the line gets so blended that there are times where it seems that both players are approaching each other or defending against each other at the same time. Someone good should elaborate/clarify on how spacing works at the top level.