Your PC can invent a new technique on his own
Taken from wikipedia's entry on the Southern Praying Mantis kung fu style:
Praying Mantis
The association of the term "Praying Mantis" with the style is also controversial. Each branch of the style offers a different explanation.
The traditions of the Chow Gar and Kwong Sai Jook Lum branches each maintain that their respective founders Chow Ah-Nam and Som Dot created their styles after witnessing a praying mantis fight and defeat a bird. Such inspiration is a recurring motif in the Chinese martial arts and can be found in the legends of Northern Praying Mantis, both White Crane styles, T'ai chi ch'uan, and Wing Chun.
If your rogue is observant enough - he may become inspired by some natural phenomenon, gaining insights about efficient and effective motions useful for offense, defense and maneuvering.
He doesn't need to be an acetic philosopher (though he may grow to become one as he advances) - he just needs the conviction and self-discipline to push him to go through the physical training required to hone his technique.
If your group's play style allows placing more emphasis on narrative at the cost of poorer combat optimization, you can even select to make the transition of your PC's reliance on his new martial skills gradual - continue wearing armor, combine armed attacks with unarmed strikes (not necessarily in the same round, though), etc. But, eventually your PC will start feeling that his armor is limiting him, preventing him from escaping blows that using his technique he can now avoid - then he may consider giving up on wearing armor. Same goes for unarmed strikes - have him hold on to his dagger, but occasionally use a flurry of blows(1) using a fist and an elbow of his other, empty hand - and let him realize that his hands have become faster and more accurate and than any weapon he is used to. This can lead him to relinquish the use of melee weapons, to use an interchanging combination of weapon and unarmed strikes or perhaps even seek "better" weapons which are more compatible with his developing abilities.
Bottom line - just because the "metagame concept" says your PC can now do something, doesn't automatically means he is aware of that and trusts himself enough to give up his old ways completely and immediately.
Or, he can find written records of a technique
Taken from wikipedia's entry on the Northern Praying Mantis kung fu style:
Origins
There are many legends surrounding the creation of Northern Praying Mantis boxing. One legend attributes the creation of Mantis fist to the Song Dynasty when Abbot Fu Ju [...] supposedly invited Wang Lang and seventeen other masters to come and improve the martial arts of Shaolin.
The Abbot recorded all of the techniques in a manual called the Mishou ("Secret Hands")
[...]
This manual supposedly disappeared until the Qianlong reign era,
[...]
The manual records Wang Lang "absorbed and equalized all previous techniques" learned from the 17 other masters.
Aside from self mastering a technique, your rogue may find a documentation of a certain technique - this can come instead of having him invent it from scratch, or as a latter supplement giving him more inspiration and advanced abilities.
At either case, you can probably work the narrative details with your GM so they won't clash terribly with the campaign settings (assuming that having a monk in it doesn't do that in the first place).
(1) Or whatever equivalent term used in 5e for that...
The unchained rogue talents Minor Magic and Major Magic only grant spell-like abilities, not spells proper nor spell lists, and spell-like abilities don't interact with the spell lists except, for instance, like in these cases, to limit the spell-like abilities the rogue can pick.
The FAQ says:
Question: Does a creature with a spell-like ability count as having that spell on its spell list for the purpose of activating spell completion or spell trigger items?
Answer: No. A spell-like ability is not a spell, having a spell-like ability is not part of a class's spell list, and therefore doesn't give the creature the ability to activate spell completion or spell trigger items.
Thus a rogue without a spell list from another source must usually employ the skill Use Magic Device to activate wands.
Best Answer
Yes, with some compromises.
The easiest way is to take 5 levels of the appropriate spellcaster. Unfortunately it is not on the Wizard spell list so Arcane Trickster is out of the question as far as RAW is concerned. But it is on the Bard list, and Bard meshes very well with Rogue. It is also on the Cleric list, and the Trickster Cleric is hella cool, and very Rogue like.
Other, more esoteric solutions.
Take the Ritual Caster Feat; pick a divination ritual, like Divination, Contact Other Plane, Augury, etc.; "reskin" the spell to be you talking to dead things.
Take the Magic Initiate Feat; pick a 1st level divination spell &/or a cantrip; "reskin" it. (Not many good options here though)
Go with the thief subclass; take use magic item; get an item that allows you to speak with the dead - you can use it 'cause you spent time with necromancers.
Get a hold of a ring of spell storing, ioun stone (reserve), or similar item. Have a friendly bard or cleric in the party. (Not as satisfying, I bet though as it is clearly not part of the character....)
Pump your Int; get expertise in knowledge skills; "reskin" skill checks as talking with the dead. If you fail a check, well sometimes the dead don't know the answer.