Any custom magic item should be priced based on its value. Different feats have different values, so I don't think any single number could be valid. Look through
Items that Grant Feats and you'll see many different prices.
The closest existing items to what you're looking for are the scabbard of keen edges, which costs 16,000 gp and the keen weapon special ability, which costs +1.
Using the suggested formula for converting spells to items with keen as a base, the suggested price is 30,000 gp. Of course, using those formulas, the scabbard of keen edges would cost 32,400 gp.
Let's take the scabbard of keen edges as a base. Unlimited use items typically cost 5/3 as much as 3/day items. Use activated/continuous items typically cost 20/18 as much as command word items. Slotted items typically cost 1/2 as much as slotless items. That would suggest the item you describe is worth about 15,000 gp.
It's a DM judgment call, but 15,000 gp doesn't seem unreasonable to me. For that price, I'd probably let you change the designated weapon once per day.