A problem I have is that I do not know what you can or need to do under UK law to will something to someone other than a family member. Thus, what I provide here is the US side of the consideration, which would at least partly apply because the property is in the US, but US law cannot determine what can or needs to be done in a UK will in relation to transfer of the property.
First, my assumptions. Since you mention "we" I assume the property is currently owned by you and your spouse and that the two you purchased it together and did nothing special to change what the deed would say about the nature of the combined ownership. In that case, the deed likely says it was issued to you and your spouse as "husband and wife," or similar, creating, under Florida law, a tenancy in the entirety, a form of joint ownership that means that if one of you dies, the other automatically becomes the full owner of the timeshare, and the property, at the time of that particular death, will not have to go through probate proceedings in Florida. That will only happen when the surviving spouse dies.
A second point to be aware of is estate taxes. Florida has none, but the US does and its estate tax laws, starting at 18% of value and going up to 40%, apply to any property in the US owned by anyone from any country. For that you should consider yourself fortunate to be from the UK. For US residents, there is an approximately $11 million per person exemption from estate taxation (double that for a surviving souse), meaning the first $11 million of the estate value is not taxed and thus most in the US do not pay any US estate taxes. The US law, however, also provides that for foreigners that exemption is only $60,000, and tax could occur if the decreased owned property in the US totaling more than $60,000 in value. However, the US and UK have a treaty under which UK residents get the same $11M exemption as US residents. Therefore, I am assuming you do not have to worry about that tax, except that if your US property totals more than $60,000, you will still have to file a tax return to claim the exemption and show nothing is owed.
Generally, you can leave the property to anyone, not just family members, with some limitations, e.g., as long as the deed is in tenancy in entirety, the first spouse that dies cannot successfully leave his or her share of the property to someone other than the spouse; also, leaving property directly to a minor should be avoided absent trusts to handle the situation. A question you need to consider before putting anything in the wills is whether you want to avoid probate in Florida. Absent some trust arrangement, the property will be subject to a Florida probate after the second spouse dies. That means hiring a Florida lawyer and incurring the expense of the probate, which itself will take time to complete. The actual person who would be responsible for taking care of that probate would be the designated executor of the estate. To avoid probate, you need a to put the property into a trust, and thus not will it to anyone. In the US, a typical mechanism for that is a revocable living trust, under which the trust becomes the legal owner of the property and a deed is prepared and filed to show that, the spouses become sole beneficiaries while living, have the power to revoke the trust during life, and then it becomes irrevocable upon death of both, and has its own provisions for how the property will then be distributed. (Note, the revocable living trust is likely something not to be used if the persons are rich and there is a real risk of paying estate tax; creating more complex irrevocable trusts are needed to avoid the estate taxes.)
The will (if you are fine with probate) or the trust can designate someone to get the property after the death of both spouses. A living trust is often a mechanism for handling most assets, not just the DVC property, after death. If you just want the property sold and proceeds distributed to your beneficiaries, you usually just designate the executor of the estate in the will or the trustee of the trust (who is often also the executor of the estate) to do that, either of whom have the obligation to make sure any sale is done correctly. Trying to designate someone else other than a relative to get the property who will then sell the property is not usual, including because (a) that someone has to outlive both of you, and (b) that someone has to be willing to accept ownership of the property and thus become liable for dues until the property is sold, but it is a possibility to be discussed with whatever lawyer you do hire to do the wills or the trust.
In any event, you should not attempt a will or a trust without legal advice, particularly when you have to deal with the laws of two countries.
As far as information you may want to leave to the designated owner about the property, other than the documents you have concerning ownership of the timeshare, it need be no more complex than explaining what you own, the obligation for dues, and providing a list of timeshare brokers that are the usual sellers of DVC timeshares.