You say 1930s Europe, and the first person who springs to mind is Magnus Hirschfeld, a gay German sexologist known for his trailblazing research on what we would now call LGBT topics. He ran the Institut für Sexualwissenschaft (Institute of Sexology) in Berlin from 1919 to 1933. While Germany under the Weimar Republic (the government during this period) was fertile ground for progressive thought, the rise of the Nazi Party made the early 1930s an increasingly bad time and place to be a researcher of this kind; the Institute was attacked in May 1933, with its books burned shortly afterwards. It's the Institute's books you see burning in this infamous photograph. Hirschfeld himself went into exile, and died two years later.
But that does still leave the first few years of the decade, with the Institute still in full function. People from around the world would visit to gain insight or professional help with their gender and sexuality; some would even take up residence for the short- or long-term. (Or even take up full-time employment there, and not just as researchers. The Institute provided employment to many people who we'd now consider to be transgender; often unemployable elsewhere, many earned a living as maids at the Institute.) A man in 1930s Europe, curious about the nature of his own attraction (or rather, his lack of it) and having the means and motivation to investigate, may well make his own pilgrimage there.
On arrival, though, what would Hirschfeld have to say to him? Hirschfeld's work on homosexuality, as well as what was initially understood as "transvestitism" (slowly evolving to consider "transsexualism", a term which Hirschfeld himself coined) are well-documented, but he has less to say on what we'd consider as asexuality. This does, to an extent, make sense in the historical context: Hirschfeld was an activist as well as a researcher, fighting against a system that would arrest people for same-sex sexual activity or for wearing the clothes of the opposite sex. Asexual people, by comparison, were still subject to the pressures of a heteronormative society (get married, have children, etc.) but did not have their lack of attraction inherently criminalised.
Regardless, outright lack of attraction does seem to be something Hirschfeld was aware of. One of Hirschfeld's first published works, in 1896, was a pamphlet titled Sappho und Socrates, Wie erklärt sich die Liebe der Männer & und Frauen zu Personen des eigenen Geschlechts? (Sappho and Socrates, How Can One Explain the Love of Men and Women for Individuals of Their Own Sex?) A forum thread on asexuality.org has English translations of excerpts from this pamphlet, and among them is Hirschfeld's acknowledgement that "there are individuals who are without any sexual desire". He terms this state "anästhesia sexualis". Hirschfield specifically brings this up when discussing differing intensities of sexual feeling: "we could make a scale similar to the scale of wind strength where 1 would be most complete indifference and 10 hurricane like sensual pleasure." He goes on to bring up hypothetical examples of how intensely people might be attracted to men and to women; someone like the man in your question might consider themselves to be at a 1 on this scale concerning attraction to men and women.
Another excerpt of interest:
It is also not possible to artificially evoke the kind of drive, that is not existent or almost not noticeable. In case of a complete atrophy there is no way that it would spontaneously develop. However, if there already is a mental disposition towards it, it can be increased by the upbringing, exercise, example, seduction and suggestion. We can wake up a sleeping drives, as long as their sprouts are big enough, but we can never create new ones. The sex drive attaches itself irremovable to the developing embryo.
This comes off as the "born this way" sort of sentiment: that someone either is or isn't born with a sex drive. If there simply isn't one there to start with, then there's no way of artificially inducing it, just as "gay conversion therapy" can't turn people straight. However, it's important to note that -- by modern definitions -- "asexual" is not considered equivalent to "having no sex drive". Asexuality specifically concerns having no sexual attraction, ie. not directing sexual desire at anyone; some asexual people do experience a sex drive, just an undirected one that doesn't involve sexual attraction to other people. In this sense, Hirschfeld's definitions aren't entirely up to speed with modern conceptions.
On another note, the 1930s are an interesting time period to have picked -- if the man in your question waited another decade (and hopped over the Atlantic to the United States), he'd see the birth of the Kinsey Scale, a model of classifying sexuality which still sees use today. Alfred Kinsey introduced the model in his book Sexual Behavior in the Human Male in 1948 (followed by Sexual Behavior in the Human Female in 1953). The Kinsey Scale is still fairly well-known, and many are familiar with how -- broadly speaking -- it measures sexuality on a scale from 0 (purely hetereosexual) to 6 (purely homosexual), with 3 (bisexual with no difference in same-sex and opposite-sex attraction) in between, but less well-known is the classification "X" that lies outside the scale entirely.
Exactly how well Kinsey's "X" relates to modern conceptions of asexuality, though, is also somewhat off the mark. While Kinsey's reports did account for sexual desire, his classifications were also based on subjects' previous sexual experiences. The "X" category refers specifically to people with "no socio-sexual contacts or reactions". There are people who consider themselves asexual and still engage in "socio-sexual contacts", for a number of reasons which don't necessarily involve sexually attracted to a partner -- anything from societal pressure to curiosity to simply wanting to give someone else sexual pleasure. While a history of sexual behaviour would list them somewhere on Kinsey's 0-6 scale, lacking sexual attraction would have them considered asexual today.