I think that's something to ask the insurer, as it will come down to how they process a claim (which would be different to each insurer). Some may require proof of purchase, some may require a "professional" evaluation of each item at the time of insuring, some may require photographic proof of the condition of the items, some might want proof of their replacement value at the time of theft (what it would take for you to replace it in a timely manner, which can be more expensive than waiting for a bargain)... while some may require all of the above.
Perhaps shop around, asking what their policy requires beforehand, and what is required when making a claim... and pick one that is easier to fulfil (as some have standard contents insurance, which would be easier to prove value and condition).

One insurer I asked at, would only offer a standard "contents insurance", and based on the (timely) replacement value, the annual premium would be $5,000! Some specialty insurers might be different, if you can convince them of Toys as being a valuable collectable. Maybe inquire at one of those insurance comparison brokers (like iselect) and they might have insurers on their database that are noted to cater for special policies.