On heating smoked salmon
As far as food safety is concered, simply warming smoked salmon or canned tuna is uncritical (tuna casserole, anyone?).

For all warm, cooked foods the two-hour rule applies: After two hours in the 40°F - 160°F (4°C - 60°C) it should be discarded. (see more here)

So it is irrelevant whether you stuff your onigiri with smoked salmon or pickeled plums, because the rice alone falls into the "potentially hazardous" category.

Now for taste:
If you manage to pack your onigiri with very hot1 rice, yes, the smoked salmon gets heated and it may be partially or fully cooked, loosing some of the "melt in the mouth" character. But unless you plan to keep your onigiri hot (which is rather uncommon, afaik), they should cool down quickly enough so that they won't overcook the salmon, leaving you with a dry center or dry flakes thoughout the onigiri. Note that the same problem would exist with pre-cooked fish. Canned tuna is beyond help anyway, as far as cooking goes...



1 And there is a limit to how hot your rice may be so that you can shape it with bare or even gloved hands...