I agree with Shaby that "eventually" the concept of the ICBM would be proven and tested by the USA, USSR, or Britain, but this development would be far less accelerated, especially in the west but even in the USSR. One reason - possibly the only reason - the German ballistic missle program received the priority it did was because Germany lacked an effective force of strategic bombers.
The USA and Britain were fully committed to the concept of strategic bombing and had aircraft capable of carrying massive loads of conventional weapons or one large nuclear bomb over very long distances. Also by 194546, bombers such as the B-29 and soon to be introduced B-50 and B-36 could operate at speeds and altitudes that rendered them difficult to intercept even by the jets of the late 1940's, and in this scenario the German advances leading to effective SAMs would not have occurred. Possibly the USSR, with their existing interest in artillery and rocketry, coupled with the fact that they lacked a large heavy bomber force, might have followed the German path but again it is hard to believe that they would have "perfected" usable ICBMs capable of delivering nuclear weapons before the late 1970's. It is just as likely that the Russians, with the "gift" of several interned B-29s in Siberia would just follow the bomber path.
Also, while rocket-propelled ICBMs might not evolve, I see no reason that the development of cruise missles would ne retarded. The V-1 (not a Von Braunian rocket) was a jet propelled cruise missile and research and development of unmanned atmospheric cruise missles would continue, creating at least a theoretical rival to the manned strategic bomber by the early 1960's. But it was only with the introduction of GPS and sophisticated computers that trully effective cruise missles that could not easily be intercepted or shot down evolved. These are dependant on satellites in earth orbit and this takes powerful rockets. Absent German reserach it's entirely a matter of speculation as to when nations would begin launching satellites. I think it's just as likely that manned strategic bombers would remain the core of strategic nuclear power through the 20th century, becoming redundant only when effective unnmaned cruise missiles - and later - reusable unnmaned bombers were developed in the 2010-20 period.