What proportion of women died in childbirth before modern times?

Short Answer

Due to the limited data (and the limitations of the data which is available), historians have come up with a variety of estimates around the period you are interested in. These estimates mostly range from around 1% to 3% per birth, depending on region and, perhaps, social background. One interesting finding is that maternal mortality appears to have been significantly higher in London than in other areas of England.

However, all of these studies need to be treated with caution, partly due to the often small size of the samples used. Also, most of it is for England though there is some data from Geneva and two locations in France which also falls within the 1% to 3% range. For Scotland, the data is even more deficient than it is for England:

Scottish population history is often a vague and frustrating subject. ...there is too little that can be said with confidence before the eighteenth century.... Deaths, or more likely burials, are the least well recorded events in parish registers of the seventeenth and eighteenth centuries:...

Details

In Milton and Maternal Mortality (2009), Louis Schwartz conveniently summarises the main studies which cover the early modern period in England (Tudor / Stuart). I've arranged these in chronological order of when the studies were published.

1971 estimate = 2.35%

In 1971, Thomas Forbes had reported a rate of approximately 23.5 deaths per 1,000 baptisms for the years 1583–1599 in St. Bartolph’s Parish, London. Since this could only have included live births (stillborn infants were not baptized), it has made sense for historians to assume that the actual numbers were somewhat higher (stillbirths often brought with them fatal complications)

1982 estimate = up to 2.5%

In 1982, in Obstetrics and Gynaecology in Tudor and Stuart England, Audrey Eccles estimated that, according to pilot studies done in the 1970s, the rate of maternal mortality in early modern England might have reached as many as 25 deaths per 1,000 “birth events” (the term covers both live births and stillbirths). In other words, one woman died for every 40 births.

1982 estimate = up to 3%

In his D. Phil. thesis in 1982, Wilson...trying to bring together early estimates of deaths in the case of live births with what he had gathered about stillbirths and other possibly fatal complications, arrived at a rate of as much as 30 per 1,000.

Also in 1982,

1982 estimate = from 2.44% to 2.9%

B. M. Willmot Dobbie estimated from parish records in Somerset rates ranging from 24.4 to 29 per 1,000.

Then, in 1986, evidence of a wide disparity between London and elsewhere.

1986 estimate = around 1%, but up to 2% in London

In 1986, however, Roger Schofield argued, in a widely influential essay entitled “Did the Mothers Really Die?,” that the national rate was actually significantly lower. He based his study on statistics from 13 rural parishes and introduced a new and more accurate way of calculating the effect that the incidence of stillbirth may have had.

Schwartz then quotes Schofield directly:

the “best” estimates suggest that the maternal mortality rate was just under 10 per 1,000 in the late sixteenth century, and just over that figure for the first half of the seventeenth century. The rate then jumps sharply upward to just under 16 per 1,000 in the later seventeenth century, to fall back to just under 10 per 1,000 again in the first half of the eighteenth century.

before adding:

He [Schofield] notes, however, that the rates in London were some 30 to 50 percent higher than in the rural samples he worked with, reaching levels of over 20 per 1,000.

Next,

1992 estimate = 1.5 to 1.6 in rural areas, 2.1% in London

In his 1992 study of maternal mortality in Europe, the United States of America, and Australia, Irvine Loudon notes the same historical rise and fall of the rate as Schofield, estimating that, before the decline, maternal mortality in early modern England was about 15 to 16 per 1,000 in rural areas and about 21 in London.

Then, in 1995, Wilson again:

1995 estimate = from 1% to 2%, depending on region

drawing on Schofield and on some research of his own, later estimated that rates for different parts of England could fall anywhere between 10 and 20 per 1,000.

Finally in England, a 1998 study of maternal mortality among British aristocrats 1600 to 1649 found that 6.8% of women from a sample of 175 died in childbirth. These women had, on average, 5 children, giving a maternal mortality rate of 1.36% per birth. However, unlike some of the other numbers cited above, this includes maternal mortality involving still births. When the author excluded stillbirths, the mortality for women born before 1700 was around 1%.

On the reasons for fluctuations over time and the significantly higher London mortality rates,

Historians are unsure just why rates rose in the seventeenth century and why they were worse in the city.

but we should certainly consider that

Birth was, in addition, experienced under highly septic conditions, the densely populated city providing a breeding ground for highly infectious diseases such as influenza, smallpox, tuberculosis, and plague. This made London a particularly hostile environment in which to be pregnant.

Source: Schwartz

Elsewhere in Europe, the French Wikipedia article Taux de mortalité maternelle cites reserach on 17th century Geneva giving a maternal mortality rate of 1.5%.

Finally, two studies mentioned in La mortalité maternelle en France au XVIIIe siècle for the second half of the 17th century show rates of 2.86% for Mogneneins in the east of France and just over 1% for Rouen in the north of France.