These are padlocks with a straight shackle rather than a U-shaped shackle. This means you just align the lock with the loop that is up inside the enclosed lock box and then just slide shackle closed. Dead easy.
Clearly you still need to measure up and ensure that the metal ring inside the lock box will fit inside the gap of the padlock and that the padlock bar is not thicker than the hole in the locking loop.
At DAM Reliable Storage & Sales we have FJM Security SPSA80-KA 3-1/8" Triple Chrome Plated D-Shaped Security locks in stock for your convenience.
These are high security insurance locks whereby you can remove a small grub screw on the side of the lock and remove the shackle entirely. The screw is simply a retaining screw so it can be removed permanently. Once unlocked and removed you put your hand and the shackle up inside the lock box and then once through the loop, attache the body of the lock to the padlock.
There is only one style of lock that does this and it is called the Granit by ABUS. Coincidentally it is also insurance approved and one of the most reliable locks on the market.
Note that in some cases the longer shackle types might give you more room to maneuver!