Pickup has to get slightly worse, you're moving the same amount of mass further away from your hands. I've always assumed people who think a short blade picks up better must just be holding the handle right at the bottom. In practice the blade length isn't the only thing that changes though, a batmaker will still balance the bat to how they like it. I'd just use the same weight, the difference will be marginal at best and pickup depends more on the individual bat and where you hold it than it does on how long the blade is.
The only way pick up improves is if you start moving weight higher up the blade to compensate
Or by reducing the length and weight of the blade.Making a longer handle and reducing the blade = net weight loss = lighter pickup. If you take it to the extreme, a bat that was standard length but 90% handle and 10% blade, would pick up incredibly light!
I've recently reverted to using a short blade bat I had made up back in 2014 and can't look back from it - likely to end up being my match bat come April 14th. The design itself is slightly different to usual as rather than being a shorter blade/longer handle, the shoulders are simply sloped down (similar to the Newbery Excalibur - effectively just involves taking a standard SH bat and dropping the shoulders either side). Pick up wise the handle and splice have been kept pretty thick so it actually picks up well for what should be a bottom heavy bat. It's probably around 1.5 inches shorter in the shoulders but obviously the same length overall as any SH. The main advantage is it weighs 2.8 and the edges are just under 40mm with the spine touching 65/70mm .I should add I'm 6ft 3", so the shorter blade/t20 style bat not being suitable for taller players is a myth in my opinion!