No other spell may be cast. Note that it's the same as the 1st level spell on the Spell Reins (closed essence) list (aside from using the weapon). Same restriction, same wording.
Also note that the Wizard has the same Spell Store effect (Arcane Companion, level 2 spell on Spell Coordination list), but also has Bypass Stored Spell as a 5th level spell, allowing the wizard to cast another spell despite having one stored (it just takes longer and more PP since they have to cast the Bypass spell first).
What's not stated in the Blade Store description, but which is stated in the Spell Store description, is that the stored spell may be cast later as an instantaneous spell. Blade Store doesn't say anything about how the stored spell is used. I would treat it the same as Spell Store. You get quite a nice advantage, at the cost of losing some flexibility.