Can a character inlay a +1 wand into a weapon and still gain its casting benefit?

I’ve been playing 5e for about a year now and recently started my own campaign DMing for a group of people that have never played before. They took to it immediately! Things have been going pretty well so far and we’ve been having a great time.

Our group’s warlock recently found a Wand of the War Mage +1. He’d like to find a high level wizard who can help him inlay it into a dagger (or, for those more flavour text oriented, a black kris blade). The goal being to then have a functioning dagger that gives a +1 to spell attack rolls. It would still be primarily a spellcasting focus, but would additionally give him a little bit of melee should he be caught in close range and not able to escape (he is a pure caster and not a bladelock so will be doing his best to avoid direct combat most of the time).

I asked my former DM (a very much RAW kind of guy) and he said NO. He didn’t really have a good explanation as to why though. I am, however, leaning in the opposite direction, If he’s willing to part with his gold I see no reason not to let this happen. Still, is there support for or against this decision?

I don’t yet have all the materials myself and was wondering if there is anything outright stated about this type of crafting (inlaying) in RAW. That being said, I would love to hear more opinions, either for or against, from some more experienced DMs.