So clearly pen and paper doesn't work, since it isn't possible to sign a transaction and broadcast the message to the network using only a pen and a paper.
Writing a software wallet would involve using third-party compilers, operating systems and hardware, which means it isn't "trustless".
It doesn’t mean “you can perform some action without trusting anybody or anything at all.” Protocols, software, hardware, and even your environment will all require various degrees of trust.
From the interactions that I've had with many supporters of cryptocurrencies on Twitter and Reddit, I don't think that this a common understanding of the word "trustless" (which literally means "without trust", by the way) within this community.
Even if we take "trustless" to mean "not trusting a single, centralised party" it's not clear at all that blockchains are trustless or even that they're more trustless than other payments systems such as Visa. That's a question that can't be answered from abstract principles. It would need to be answered empirically.
Of course it will depend who you ask; but most Ethereum developers at least would probably agree that the word “trustless” shouldn’t be interpreted literally as “without trust” to the extent your comments suggest, just as “serverless” systems might still involve servers. Call it a misnomer; there’s plenty in the English language.
Writing a software wallet would involve using third-party compilers, operating systems and hardware, which means it isn't "trustless".