The issue of touching a woman when sexual intercourse is forbidden is addressed in Shulchan Aruch Yore Deah 195, sayf 17; Shach Sayf Katan 20; Gemara Shabbos 13; and the main discussion is in Sefer Hamitsvot of Rambam lavim 353 with the objections of the Ramban. All the prohibitions of non-sexual contact are bounded to a sexual risk.
The Gemara Shabbat says about prohibited period (nidda).
(But he is self-contradictory, for) 'Ulla said, Even any form of intimacy is forbidden,because we say, 'Take a circuitous route, O nazirite, but do not approach the vineyard.
But your question addresses contact with a not niddah woman who is not prohibited as Arayos, e.g. a celibate, unrelated... etc. What is the kind of this problem?
See in Rambam
Sefer Nashim Hilchoss Ishus Perek 1 Halacha 4
Before the Torah was given, when a man would meet a woman in the marketplace, and he and she desired, he could give her payment, engage in relations with her wherever they desired, and then depart. Such a woman is referred to as a harlot.
When the Torah was given, [relations with] a harlot became forbidden, as [Deuteronomy 23:18] states: "There shall not be a harlot among the children of Israel." Therefore, a person who has relations with a woman for the sake of lust, without kiddushin, receives lashes as prescribed by the Torah, because he had relations with a harlot.
Regarding concubinage, Rambam Melachim 4.4.
Similarly, he (the King) may take wives and concubines from the entire territory of Eretz Yisrael. The term 'wives' implies women who were married with A ketubah and kiddushin; concubines, women who were not given A ketubah and kiddushin. With the act of yichud alone, the king acquires her and relations with her are permitted him. A commoner is forbidden to have a concubine.
But the Ramban in teshuva, quoted in Kesef Mishne Ishut 1.4 and in Abudarham, Hilchot Berachot, Birkat Erusin says that a commoner is allowed to have a concubine. Further the Ramban concludes that despite he holds that there is no prohibition for a commoner, he cannot take a concubine because this will lead them to sexual intercourse in the Nidda period.
If the woman is potentially permitted (neither erva nor nidda) a non sexual touching is allowed deorayta. But there is a problem with touching sexually oriented, even looking and speaking. We need to read this Gemara Sanhedrin 75a, wich is ruled by great Rishonim (Rambam, Rosh).
Rab Judah said in Rab's name: A man once conceived a passion for a certain woman, and his heart was consumed by his burning desire [his life being endangered thereby].
When the doctors were consulted, they said, 'His only cure is that she shall submit.'
Thereupon the Sages said: 'Let him die rather than that she should yield.'
Then [said the doctors]; 'let her stand nude before him;' [they answered] 'sooner let him die'.'
Then', said the doctors, 'let her converse with him from behind a fence'.'
Let him die,' the Sages replied 'rather than she should converse with him from behind a fence.'
Now R' Jacob B'Idi and R'Samuel B'Nahmani dispute therein.
One said that she was a married woman; the other that she was unmarried.
Now, this is intelligible on the view, that she was a married woman, but on the latter, that she was unmarried, why such severity? - R'Papa said: Because of the disgrace to her family.
R'Aha the son of R'Ika said: That the daughters of Israel may not be immorally dissolute.
The Rambam concludes hallachically (Mada, Yesode Hatorah 5, 9; reported in Bet Yosef YD 157, but not in SA). Bet Yosef understood that Rambam ruled that despite the rule to be lenient for a doubt about a question that has a lethal issue (the doubt is if the prohibition regards also an unmarried woman), since the stringency is to do nothing, not an act (to leave the man ill is not an action), we need to be stringent. The Rosh ruled as Rambam {anyways in Shulchan Aruch Poskim did not report this rule concerning an unmarried woman as @mevaqesh enlighted. They did not state the prohibition to heal up a life threatened man with looking or speaking with a unmarried woman, but they don't allow at all to make this overall}:
Here is a translation of the Rambam.
[When] someone becomes attracted to a woman and is [love-]sick [to the extent that] he is in danger of dying, [although] the physicians say he has no remedy except engaging in sexual relations with her, he should be allowed to die rather than engage in sexual relations with her. [This applies] even if she is unmarried.
He is even not to be given instructions to speak to her [in private] behind a fence. Rather, he should die rather than be given instructions to speak to her behind a fence. [These restrictions were instituted] so that Jewish women would not be regarded capriciously, and [to prevent] these matters from [ultimately] leading to promiscuity.
Chachamim prohibited very strongly a very light kind of contact when it is motivated by sexual drive.