I think the decals just have to be publically available, not necessarily by yourself.
But, I can't see how to re-share a livery once I've got it from GTS
Just on the off chance, this benefits somebody else, I have found out how to retrieve my liveries from my alternative account.
I made almost all my liveries on GT Sport when I lived in Asia, and therefore on my Asian account.
I want to make use of them (and have them updated( to use on my European GT7 account.
Asian GT7 Account
In the livery editor, select open design and then select 'All' from the option in the top left-hand corner. Here I can see all of the GT Sport liveries that I shared when I played GT Sport. Once I open a livery in GT7, the next livery becomes available. If like me, you had similar liveries, with colour changes, or a few duff liveries, delete them. The 100 most recently available liveries are kept available. These are updated, almost in real-time. Just have to exit and return so that the list is refreshed.
Yes, I have to buy the cars on my alternate account, but with circuit experiences, and the sport time trail - getting a million credits every so often is quite fun.
When I open the livery, go to edit to replace any missing decals - opening the image from GT Sport shows the front and side, so this isn't too hard or time-consuming to do. So far, only one or two of the decals need replacing, and so adding this to the favourites makes this process a little more efficient.
Save the livery, as a style and share. I had the account name in the tags to make them easier to find.
I realize most will have realized all this, but I'm sure somebody might find this useful