Not necessarily owned by an Omani. Many countries traded thru Zanzibar including the Omanis.
Why do you think that the grip was ivory? Could just as easily been bone or giraffe hoof, or for that matter a wood of some sort. If it was ivory (suggesting a high class owner) it would also point to the grip dressing being silver. From your photos it would appear that the grip is not silver.
Could you post a photo of the whole sword please.

As well noted by Kahnjar, Zanzibar was a key trade center in the 19th century and of course being an Omani sultanate, there were considerable numbers of the types of edged weapons commonly in use in Arabia in that context.

The Persian shamshir was a highly prized sword by Arabs throughout the Dar al Islam, so presence of this example in Zanzibar is not unusual. It seems unusual that the hilt material is gone as I thought bone, ivory etc. would survive in an archaeological deposit. More likely of course the ivory would have been taken for its value and the sword discarded.
By the same token, if the hilt was silver, that too would have been taken.

Always fascinating when any weapon is found in situ, and speculating how, when and why it ended up where found. Thank you for posting this!

It's worth bearing in mind the climate of Zanzibar. It's a tropical island six degrees below the equator. It has two rainy seasons with torrential rain and flooding. Annual rainfall is av. 1684 mm (compared to 1,168 in the UK). So Zanzibar gets nearly 50% more rain than the UK. So it can be very wet and humid. The average temp. is 25 - 30 degrees C.

So the sword would have been exposed to a lot of water while in the soil. Imagine what those conditions would do for between 300 and 500 years...

At the earliest, this blade could be late 17th c. Much likelier mid-late 18th century. The guard is 18th century. Where it was found doesn't impact its origins, it is Persian, plain and simple. That it was carried (and apparently lost) in Zanzibar is an interesting side note, but that is all you can say about it. On the other hand, if the blade were inscribed for example, MY NAME IS MUSTAFA, I'M OMANI AND THIS HERE IS MY SWORD, you could make a case for such an attribution.

There are excavated ivory artifacts dating back over 40,000 years which are surprisingly intact. No type of ivory I'm aware of degrades easily or quickly. Assuming the grips were ivory, which is far from certain unless there were particles attached to the tang, this sword lost its grips before it was... interred, as it were.... They were just as likely to be horn or wood.

An overall image would be helpful.