Material hunting

Yes

Don't chose steel.

Steel has relative density of 7.8 but actually may be between about 7.5 to 8.1. You want 10.

You can not have steel and density both. You have to compromuse on something

Of course you may have a sealed steel capsule with something heavy inside to have a apparant density of 10.

May be high tungsten or platinum steel alloy can fall in that range,

Hastelloy