How to use local variable as a type? Compiler says “it is a variable but is used like a type”

You were very close, you were just missing a call to MakeGenericType.

I believe your code would look like the following:

Type t1 = v1.GetType().GetProperty("Value").PropertyType;
var shellPropertyType = typeof(ShellProperty<>);
var specificShellPropertyType = shellPropertyType.MakeGenericType(t1);
dynamic v2 = specificShellPropertyType.GetProperty("Value").GetValue(v1, null);

Edit:
As @PetSerAl pointed out I added some layers of indirection that were unnecessary. Sorry OP, you probably want a one liner like:

dynamic v2 = v1.GetType().GetProperty("Value").GetValue(v1, null);