what's considered overkill for spd?

There isn’t. The spd meta keeps getting worse and worse so you need all you can get.

But to me, once you go over 51 (doubling 46) is a sign that it’s pointless to further invest in speed

It is hard to overkill on speed these days, but not impossible, and generally speaking I think 52 speed truly is overkill, especially if Shigure is getting flier buffs. (Literally nobody needs 56 or 58 speed.) Even if he's not getting flier buffs, he should function more than fine in the upper 40s, so he might appreciate the attack boon more. I will acknowledge that units do seem to keep getting faster and faster, so it's possible a +spd version would have a longer shelf life, but for now and in the immediate future I think +atk would serve him just fine.

Speed in arena isn't insanely high unless you reach +10 whale tier. For stupidly difficult challenge content in the game where all random enemies are buffed up on steroids that got buffed up from more steroids, that's when you start considering those crazy numbers, but even then I'd say 45 spd total +any A, B, or C slot skill activation would be good enough from experience. I'd keep the +spd IVs, since having speed is most important for securing them one turn kills, especially on units like Shigure. Having one unit alive could ruin everything, and that's about the worst that could happen.

42 is the magic spd number, only a handful of units will go way over it, while everything else will simply not double at all. More investing more than 42 is mostly a waste unless you're ayra, and any less and you risk getting doubled more often.

70 spd

Speed Creep is getting worse as time goes. It's true that you can fix an issue with a B skill (Lancebreaker, Swordbreaker or QR) but there are other skills you'd like to have there instead.
About how much speed you need to double, it depends on what type of content you're doing. Fast units in high T20 usually run Distant Counter to get those points, sacrificing potential speed. (They also run other things, of course).
Another thing to consider is the inflated stats of LHB or GHB and, the most recent, Max Infernal GC units who reach really high speed values and are harder to double.

What units do you want Shigure to double, and which do you want to avoid doubles from?

Really, this is the only question you should be asking. If you want him to double the fastest sword users, you probably need to go all in. But there are other ways to deal with them. For instance, if you can just avoid their double, you can bait them, take a hit, return fire to get them low, then finish them off on your turn.

There are also some extremely meta defining skills to take into consideration when you think about speed. Bold Fighter circumvents it, so your speed will do nothing to stop the double. Likewise, when attacking, Quick Riposte will ensure you get hit twice.

I'm a bit late to notice your question, but you will probably find this helpful:
https://fireemblem.gamepress.gg/q-a/karlas-generation-analyzing-spd-powercreep