This answer covers herpes, with both HSV1 (usually appearing and transmitted orally) and HSV2 (usually called genital herpes).
So-called "asymptomatic shedding", when the virus can be transmitted despite the carrier not showing any sores, is unfortunately very common in both herpes types.
An in my opinion good article is Asymptomatic Shedding of Herpes Simplex Virus 1 and 2: Implications for Prevention of Transmission. It given an overview over several studies, for example one where 144 heterosexual couples where only one partner was infected were tracked.
Transmission occurred in 14 (9.7%) of the couples, including 13 in which diaries were maintained during the period when transmission occurred. Although 4 couples (31%) reported sexual contact during the prodrome (1 case) or within hours before lesions were first noted by the symptomatic partner (3 cases), in 9 cases (69%) transmission resulted from sexual contact when the source partner reported no symptoms or lesions
PCR studies, looking for genetic material of the virus in the genital regions of infected but asymptomatic people confirmed that asymptomatic shedding is common:
asymptomatic shedding from anogenital sites was documented in 80%–90% of seropositive men and women, was present on ~20% of days with daily sampling, and was present at even higher frequency during the first 3 months after acquisition of first-episode genital herpes
The samples in these studies were daily swipes of the vulvar or penile region. Studies usually checked for lesions or open cuts.
There are also studies were multiple samples were taken each day:
Anogenital shedding was detected on 20% of 962 days, and the median duration was 13 h. Oral shedding was detected on 12% of 691 days during which all 4 samples were collected, and the median duration of shedding was 24 h.
The CDC factsheet on genital herpes basically agrees with this, saying:
Transmission most commonly occurs from an infected partner who does not have visible sores and who may not know that he or she is infected. 4 In persons with asymptomatic HSV-2 infections, genital HSV shedding occurs on 10% of days, and on most of those days the person has no signs or symptoms
As for your two specific questions:
Possible transmitted diseases if saliva/semen/pre-cum/etc is swallowed?
Herpes can be transmitted during oral sex, both from oral herpes being transferred to the genitals, and from genital herpes being transferred to the oral region.
Possible transmitted diseases if fluids (pre-cum/semen/saliva/etc) are spilled on the vagina, or the head of the penis?
That's how herpes occurring in the genital region is usually transferred, even in the absence of sores (see above), so in that way herpes fits your criteria.