As long as you know how shiny calculations work, and how to transform the new version TrainerID/SecretID into their old versions (which are what is used when calculating shinies), yes.
One way to do that:
- Before starting, find a program that can convert numbers from decimal to hex, and that can do the XOR operation. The Windows 10 calculator does that in Programmer mode.
- Go into the OT/Misc tab. Jot down your 4-digits SID and 6-digits TID, and put them together (so, for example, if you had SID=1234 and TID=567890, the resulting number would be 1234567890). Important: the 6-digit TID can start with one or more zeroes, don't remove those.
- Convert that number to hex; this is your trainer's full ID, and the number that is compared with the pokemon's PID to determine if the pokemon is shiny. In the current example, it would be 499602D2.
- Choose a 4-digits hex number and write it twice; for example, if you choose ABCD, then you would get ABCDABCD.
- Now calculate the XOR of that number you got and your full trainer ID; in the example, 0x499602D2 XOR 0xABCDABCD is E25BA91F.
- Put that number you calculated in the pokemon's PID, in the Main tab. Now you have a "square shiny".
If you want it to be a regular shiny, when writing twice the 4-digits hex number, change the last digit. In the example, it would be ABCDABC?, with the ? being anything except D.