"Operational" and "in service" are two very different definitions. The I-16 was put back into production in 1941 and was produced until 1942. In 1941 just over 2,000 I-16's were in service with the Soviet Air Force. More than 8,000 I-16s of all marks were produced in total. More than one and a half thousand of those were two-seater trainers that served until the 1950's. So I wouldn't say it is unreasonable to believe the claim that about half of the produced I-16s were still in service (at some point) in 1943.
Actually 10,278 of all types of I-16 have been produced (please, see the table) , but the modern types were only I-16 Type 18, 24, 27, 28, 29 produced in 1939-41 with M-62 or M-63 engines. The total number of modern versions produced is 2,113 and the "hybrid" type of these versions is modelled in AH. You may also noticed that the production of I-16 was shutting down in 1941 as only 19 of Type 24 and 80 of Type 29 were built and the rest were Type-15 (Uti-4) two seater trainers. That is the reason why the operational (or as you wish "in service") numbers of I-16 reduced to 240 in the end of 1941 as I mentioned before. Sure I-16 played a significant role in 1941, but do not overestimate it as, for example, MiG-3 was produced in 3,000+ numbers in 1941. In 1942 the numbers of I-16 in service reduced to insignificant values and in 1943 the few squads which were still equiped with I-16 were re-equipped with new Yaks, LAs or P-39s.