It is likely not a hachana problom. Hachana is in genaral only a problom if what you are doing cannot be done after Shabbos. However since if you are not going to fold the tallis it will get all creased and ruined it is not preparation for after shabbos it is simply causing the tallis to not get wrinkled which can only be done now.
The Issur falls under the melacha of mechabes – or laundering. Part of the laudering prosses in the time of chazal/the mishkan was to fold. After they would wash the clothing it would be place somewhere on a creace and it would stay like that for a long time until it molded the the clothing so to speak. Keep in mind theye did not have clithing like we have now it was more large peices of material which without these fold would not havee much shape. As such many rabanom forbid folding a clothing item where you want the crease. SO for example folding a polo shirt would not really be part of the laundering prosses because you ar just folding it for organazation not because you want the crease. Folding suit pants however or a tallis are ussually the examples given where folding on shabbos would be problomatic. Thus you can probobly just fold it slopely or not on the creace this may avoid the problom. Colsult your compatent local rabbi.