If you can, I would recommend that you change the PK definitions in the target database - they should be defined as int, but NOT identity.

Why? So that the PKs in the source table can be inserted into the target table, meaning that you can do a direct match from one to the other.

Is it safe to assume that there will be no updates to existing rows in the tables?

A script along the following lines should do it (if you make the change I suggested), assuming DbSample1 is source and DbSample2 target (untested and incomplete):

declare @MaxId int

--Get the MaxId from table1 in target database

select @MaxId = (select max(pKey) from DBSample2.dbo.TabSample1)

--Insert all the rows from table1 in source database whose ID is greater.

insert DbSample2.dbo.TabSample1(pKey, col1, col2, ...)

select pKey, Col1, Col2, ...

from DbSample1.dbo.TabSample1

where pKey > @MaxId