Soulstrider, there's a few things which might work.
Best would probably be increase your country size by adding regions until you can laugh in the face of the HRE armies.
Prior to that, sneakiness is required.
First, let's assume your Italian target has enemies of its own. It might want to conquer someone/regularly war dec someone. Ally with that someone so you can get into a defensive war with your Italian target. As your target is the aggressor, not you, the HRE will not be called in (probably at least). You win the war, annex your target, suck up the infamy cost.
Second sneaky plan, hope for a CB on someone else in the HRE in addition to your target. Let's assume you're trying to annex HRE member Mantua, & have a Conquest CB on them. Let's assume you get an opportunistic CB (say a Border dispute, violated sphere, or whatever) on HRE member Venice, about whose territory you don't care a jot. What you could do is - on the same day - war dec first Venice then your real target of Mantua.
The AI can only ally against you in one war, the first one. So you'll find yourself in one war against Venice & probably the entire HRE, & in another against just Mantua. You make a WP asap against the alliance leader in the Venetian war (& to do this may be difficult, you may need to concede defeat if not careful), then after that happily trouce Mantua. In a situation like this, it would probably pay to mass your armies ready for the Venetian war, to make some initial rapid gain that will get you the WP before the massed ranks of the HRE descend on you.
Other than that, the other things to try would be to ally with the HRE leader & Milan yourself, get good relations with them, make powerful allies elsewhere, & just hope for the best when you war dec your target. Doing that in conjunction with sneaky plans A or B is probably a good idea anyway.
Also, if you do seize an HRE region, you might want to consider googling "Unlawful Imperial Territory" - if you're not in the HRE & take an HRE member, it's probably best to remove the region from the HRE asap using a magistrate, else you get a rather nasty regional event where the HRE demands the region back.