"We will build a custom hood cover on top."

Then you would want a Range Hood Insert. It's generally recommended that a range hood be 3" wider on each side than the cooktop so a 42" insert would be appropriate. Among Vent-a-hood range hood inserts the 19-1/4" deep BH240SLD SS or M40SLD SS would probably be appropriate but you could go with the 22-1/4" deep BH240PSLD SS if you wanted a hood with greater coverage.

Don't forget to set the bottom of the range hood at the hood manufacturer's recommended height above the cooktop.

For capture, hood overlap of cooking plumes is desirable; for containment of captured plume effluent, adequate CFM is desirable. If you stir fry or sear, then 90 CFM/sq. foot of hood entry aperture is appropriate. Otherwise, you might get away with 60 using induction.

Do you intend to use VaH Magic Lung designs, or more conventional blower designs with hood baffles near the hood base? This will determine the rated blower performance relative to the desired/require blower performance.

What about noise? For best suppression of blower noise, a duct long enough to include a silencer is needed, as well as an outside or at least downstream in-line blower.

Are you aware that you will need a make-up air system or configuration (except under exceptional circumstances)?