I think altho it can be said to be overkill in this situation, sterilising soil is always a good idea since it doesnt bother you much and gives you the peace of mind problems dont arise out of the soil, thats especially true with soil you collected outside or a bag you opened a longer while ago. Same applies to pots, you can always boil / microwave / expose to any DNA cracking radiation ... And so on. Especially in high humidity applications all this comes handy (morning glory is not in that category as far as Im concerned).
As for anti mould, no one would use pure H2O2 on seeds, not only is it hard to obtain, seeds would also react violently and be destroyed in a matter of moments. Anyway im no fan of H2O2 for its anti mold properties anyway, and for chemical scarification its not a good choice too, I use this (see attachement please) I must try to find out what it is called in english, I can tell you its a anti-fungus substance that has originally been invented for human inner and outer treatment, it has been discovered that ingesting it really is a thing you dont want, so its now sold in pharmacys for external treatment, altho there is better substitutes. So its solely purpose today is
plants, even orchid seeds like it no matter what youve done to them first, same applies for cacti.
Edit: one last thing to mention, most fridges are highly contaminated with funghus and bacteria, ince we store so many things in there they might like. The temperatures may inhibit excessive growth, but they do grow and spread ... I think everyone can testify. Also most fridges are set too warm and for theese reasons the manufacturers recommend cleaning a fridge on a monthly basis. So storing seeds in it for a longer span of time will lead to multiple contamination (if not sealed). You wouldnt store food for that span of time in it and expect it to be okay wouldnt you ?
I hope I could offer some usefull information.