Don't let the spy do his rounds tbh. It's already not that hard to know that a spy exists, he needs some time to reach your base after being bought, and with this patch he is also much more fragile so the only "combat" he is really suited to is picking off the unaware from the shadows before they can notice him - if anyone is aware of his presence he is really easy to deal with. But even then, if there's a spy going around your base unmolested hitting up all the buildings because your entire team is on the front lines, then that means the Allies have one less tank/rocket/Tanya/whatever able to sit around and defend from whatever's coming their way. That was a pretty big problem with spies before - most of their contributions for their team were absolutely not worth giving up an extra combatant for, especially if the Allies are stuck on the defensive which is more likely when they have less manpower to push out to the field. Oh good, manifest says the Soviets have 5 mammoth tanks, we kinda already gathered that from their limited war factory purchase pool, would have much rather had a medium tank/rocket at home to actually deal with that! And if your base is completely empty so anyone wanting to infiltrate will have a field day, would you much rather that the infiltrator was a spy signaling your sneak attack, or a phase-thief destroying mines and stealing half your credits, or a phase-tanya or phase-engineer destroying a building?
I'd be open to maybe adding a slight delay for the hacking, but an absolute no to letting the Soviets know that they've been spotted. Soviets not knowing that is kind of the entire point.
You can't get airdrops with a relay. And if Allies want to get radar back, they have to render themselves one tank/tanya/rocket/other-inf-of-choice short for as long as it takes the spy to reach the enemy base, which on most dome maps is a fairly long time even if the spy is taking the shortest possible route which would almost certainly involve running past multiple Soviets, at least one of whom should recognise him.
If the other spy abilities get a chargeup delay I would do it for this one too just for consistency. I had only considered it for the refinery ability initially because of how incredibly powerful it is and the fact that its eventual effect can be pretty heavily delayed by killing ore trucks.
The "one man down = gg" and "spy is easy to spot" arguments may be less applicable to larger games; however, it's been a thing for all of Delta that map victories have gotten more and more skewed in the Soviets' favour the higher player counts get. The spy seemed a pretty obvious choice for a unit who could be buffed to help give Allies a bit more of a fighting chance in larger games without suddenly causing the Allies to dominate small games. You really can't afford to dedicate someone to "reveal the sneaks/slow the economy/get the radar back" duty in a 4v4 unless there's a pretty severe player skill imbalance.