There are a number of approaches to this, depending on exactly what you want to achieve.
There are dense castable refractories which will operate up to 1800C. For small quantities the best source is likely to be a ceramic kiln supplier. Industrial foundry supplier may have a wider range of products but tend to deal in larger quantities.
Another possible alternative is graphite, this needs to be shielded from oxygen to prevent oxidation, but then again so does molten titanium so you would need to do that anyway as titanium is very prone to porosity and embrittlement due to absorbing atmospheric gasses, even at temperatures well below its melting point.
Zirconia based refractories can also work well at very high temperatures. One option is to use a sofer insulating refractory, or indeed rigidised ceramic wool which is coated with a layer of zirconium slurry, this is the principal behind ceramic shell investment casting.
It is also possible that any shielding gas used will also provide a significant cooling effect and as such you may find that the case temperature is significantly less than the molten metal temperature, especially as pressurised argon will give you a significant cooling effect for free.
As an aside I'm not sure how much work you have done on the whole concept of extruding molten titanium through a nozzle but it seems a bit iffy to me as I am not aware of any current process which does anything remotely like this and for absolute certain in TIG welding any contact between the tungsten electrode and the base metal is normally considered a defect as the base/filler will instantly alloy with the tungsten and contaminate it.