IMPORTANT NOTE
You will require both of the following mods for this guide to apply:
https://steamproxy.net/sharedfiles/filedetails/?id=2129157917 (SP Circus Trinkets)
https://steamproxy.net/sharedfiles/filedetails/?id=2325415039 (Ringmaster Class)

1. Go to (drive):(folder)Steamsteamappsworkshopcontent2620602325415039loot and open ringmaster.loot.json

2. In ringmaster.loot.json, change arena_SP_IMP to arena_SP

3. Go to (above file address)trinkets) and delete both arena_SP_IMP.entries.trinkets.json and arena_SP_IMP.rarities.trinkets.json

4. To really seal the deal, go to (above file address)\panels\icons_equip\trinket) and search SP_IMP in the file browser in that folder, then delete every result.

After these steps, using Ringmaster's Camping Skill "Ringmaster's Prizebox" should directly give you a trinket from the Singleplayer Circus Trinkets pool.

Please comment if this guide is not detailed enough. If so, I will update with images.