I believe that there isn't an association between strings on toys and shoelaces. Two of our cats (Hunter and Juliet) would rather play with the strings on wand toys than whatever the strings are attached to (feathers or whatever), but they haven't really carried that connection to other similar objects.
We first knew that we had a problem with strings when we tried a specific type of toy. There are some toys that are meant to be tied to a doorknob and left, a string (or elastic) will help keep them entertaining for the cats without your direct participation. Hunter and Juliet just sat there chewing on the string until it broke, and then they tried to eat the string. Yet, we leave random string objects around the house all of the time and they don't mess with them (I looked around the living room this evening and found charging cables for various electronic devices, lanyards from conferences/events, a soft measuring tape, and other string like objects). Our cats have never made the connection between these objects and their string toys.
One thing that I do try to do is pay attention to their body language, and if they get that attentive "I'm going to jump on something!" look when looking at something that is Not Their Toy, we try to focus their attention elsewhere so they don't make the connection that (for example) the drawstring on my pajamas is a toy. The methods (and success) differ depending on each cat and their personality. For example, Hunter thinks the sun rises and sets on whatever my husband wants, so if he tells Hunter "no", Hunter will stop whatever it is (and sulk a bit). Kendall is still very young and kittenish (by my standards, he's about 4), so I generally have to give him something that IS his toy to distract him. With most of the cats, we don't generally try to punish them, but try to focus more on redirecting (give me that, here have this instead).
I think that an existing belief that shoelaces are toys can be retrained. When we first got Juliet, she also loved to chew on electrical cables. We went through, removed all of the cables we couldn't supervise (or covered them in protectors), and gradually broke the association. After about a year of paying close attention to it, she was apparently out of the habit of it, because now we leave cables and stuff out all of the time without any harm.
Most behavior problems can be lessened by giving them more play, so if they have enough playtime they are less likely to be looking for hunting opportunities at other times. One thing I've seen people do is put a wand toy in their belt loop as they move around the house cleaning (or whatever), which can lessen the time investment for you and may focus their attention on the toy rather than your shoelaces, but it may just train them to be underfoot when you're busy. I haven't ever done it regularly (some times when I'm playing and have to go stir something on the stove or change laundry I've done it, but not as a regular thing).
The last suggestion I have is if they are playing with your shoes in your bedroom while you're trying to sleep, train yourself to put your shoes away. Ginger likes to lick plastic (bags, tape, all sorts of things), so we have to look around the bedroom for things she might lick in the middle of the night. It's annoying, but she doesn't wake us up with rustling plastic sounds.