Your question:
How to reduce injection molding tooling cost?
(Do you think if we do any kind of CAE or any other work related to injection molding tool will help us to reduce cost?)
If you like to use the toolmaker only as your workbench - May be
But !
"I am sure a toolmaker would love you to do this as it then absolves him of any responsibility as to it's function"

I have also some other recommendations (ATTENTION: POLEMIC !!!)
- make all moldflow and complete drawing of the mold / tool
- supply the steel to the toolmaker and care for the heat treatment
(if you by a lot of tools you can make an agreement with the steelmaker and get some extra bonus)
- supply all components to the toolmaker (limit switches, hydraulic cylinders, ejector pins, hot channel ...)
- make the sampling of the tool in your plant
- make the dimensional report in your plant
- make all final adjustments in your plant
- make all documentation (drawings, handbook) and spare parts by yourself
- take care about all accessories for handling
Please don't forgot: manage by yourself all changes from final customer
Your toolmaker "would love you" - he has to think only about machining and assembly
Sure, you don't have any problem to manage all this activities and you will get the tool in SHORTER times with BETTER quality and CHEAPER than from your toolmaker.
BUT SEROUSLY:
why everybody is asking for price reduction (at the end you get what you paid for) and
nobody is asking how to improve the mold.
A well done mold with good components from a good toolmaker will cost more, but this tool can make you save a lot of money during the lifetime of the tool (lower cycle time, less downtime for maintenance, less scrap - you will save a lot of money - but OK, it's very difficult to calculate and demonstrate this savings, it's easier to demonstrate the reduced tool price).